Hoon Hong

Works (108)

Updated: February 19th, 2026 22:57

2025 article

Equi-affine minimal-degree moving frames for polynomial curves

Hong, H., & Kogan, I. A. (2025, November 1). Journal of Symbolic Computation.

By: H. Hong*  & I. Kogan* 

topics (OpenAlex): Mathematical Analysis and Transform Methods; Advanced Numerical Analysis Techniques; Geometric Analysis and Curvature Flows
Source: ORCID
Added: November 20, 2025

2025 article

Geometry of Continuous Adjoint Newton's Method for Bivariate Quadratics

Hauenstein, J., Hills, C., Hong, H., & Carrion, F. P. (2025, August 1). Maple Transactions, Vol. 5.

By: J. Hauenstein, C. Hills, H. Hong*  & F. Carrion  n

topics (OpenAlex): Advanced Numerical Analysis Techniques; Iterative Methods for Nonlinear Equations; Advanced Measurement and Metrology Techniques
Source: ORCID
Added: July 25, 2025

2025 journal article

Geometry of Continuous Adjoint Newton's Method for Bivariate Quadratics

Maple Transactions, 5(3). https://mapletransactions.org/index.php/maple/article/view/22493

By: J. Hauenstein, C. Hills, H. Hong  & F. Carrion

mapletransactions.org
Source: ORCID
Added: July 17, 2025

2025 article

Improving angular speed uniformity of rational parameterization using piecewise radical reparameterization

Hong, H., Wang, D., & Yang, J. (2025, March 27). Annals of Mathematics and Artificial Intelligence, Vol. 3.

By: H. Hong n , D. Wang * & J. Yang *

author keywords: Rational parameterization; Angular speed uniformity; Uniform parameterization; Piecewise radical transformation
topics (OpenAlex): Advanced Measurement and Metrology Techniques; Optical measurement and interference techniques
Sources: Web Of Science, NC State University Libraries
Added: April 7, 2025

2025 article

Relations among multi-polynomial subresultants

Hong, H., Meng, J., & Yang, J. (2025, October 9). Journal of Symbolic Computation.

By: H. Hong n , J. Meng* & J. Yang *

topics (OpenAlex): Polynomial and algebraic computation; Commutative Algebra and Its Applications; Advanced Differential Equations and Dynamical Systems
Source: ORCID
Added: February 7, 2026

2025 article

Robust parameter estimation for rational ordinary differential equations

Bassik, O., Berman, Y., Go, S., Hong, H., Ilmer, I., Ovchinnikov, A., … Yap, C. (2025, July 28). Applied Mathematics and Computation, Vol. 509.

By: O. Bassik *, Y. Berman*, S. Go *, H. Hong n , I. Ilmer *, A. Ovchinnikov *, C. Rackauckas *, P. Soto *, C. Yap *

author keywords: Parametric ODE models; Parameter estimation; Differential algebra; Symbolic-numeric differentiation; Mathematical software
topics (OpenAlex): Control Systems and Identification; Advanced Control Systems Optimization; Probabilistic and Robust Engineering Design
Sources: ORCID, Web Of Science, NC State University Libraries
Added: July 28, 2025

2024 article

Computational Algebra and Geometry: A special issue in memory and honor of Agnes Szanto

D'Andrea, C., Hong, H., Hubert, E., & Krick, T. (2024, December 17). Journal of Symbolic Computation, Vol. 129.

By: C. D'Andrea *, H. Hong n , E. Hubert * & T. Krick *

topics (OpenAlex): Mathematics and Applications
Sources: Web Of Science, NC State University Libraries
Added: January 21, 2025

2024 article

Improving Angular Speed Uniformity by Piecewise Radical Reparameterization

Hong, H., Wang, D., & Yang, J. (2024, January 19). Electronic Proceedings in Theoretical Computer Science, Vol. 398, pp. 165–178.

By: H. Hong n , D. Wang  n & J. Yang  n

topics (OpenAlex): Advanced Numerical Analysis Techniques; Manufacturing Process and Optimization; 3D Shape Modeling and Analysis
Sources: Web Of Science, NC State University Libraries
Added: April 1, 2024

2024 article

Parametric “non-nested” discriminants for multiplicities of univariate polynomials

Hong, H., & Yang, J. (2024, March 8). Science China Mathematics, Vol. 3.

By: H. Hong n  & J. Yang

author keywords: parametric polynomial; complex roots; discriminant; multiplicity; resultant
topics (OpenAlex): Polynomial and algebraic computation; Matrix Theory and Algorithms; Mathematics and Applications
UN Sustainable Development Goals Color Wheel
UN Sustainable Development Goal Categories
10. Reduced Inequalities (OpenAlex)
Sources: Web Of Science, NC State University Libraries
Added: April 8, 2024

2024 article

Smooth connectivity in real algebraic varieties

Cummings, J., Hauenstein, J. D., Hong, H., & Smyth, C. D. (2024, October 5). Numerical Algorithms, Vol. 10.

By: J. Cummings *, J. Hauenstein *, H. Hong n  & C. Smyth *

author keywords: Connectivity; Smooth points; Real algebraic sets; Polynomial systems; Homotopy continuation; Numerical algebraic geometry
topics (OpenAlex): Polynomial and algebraic computation; Commutative Algebra and Its Applications; Algebraic Geometry and Number Theory
Sources: Web Of Science, NC State University Libraries
Added: October 14, 2024

2023 article

Erratum for “Global Identifiability of Differential Models”

Hong, H., Ovchinnikov, A., Pogudin, G., & Yap, C. (2023, September 22). Erratum for “Global Identifiability of Differential Models.” Communications on Pure and Applied Mathematics, Vol. 9.

By: H. Hong n , A. Ovchinnikov *, G. Pogudin * & C. Yap *

topics (OpenAlex): Polynomial and algebraic computation; Advanced Differential Equations and Dynamical Systems; Mathematical and Theoretical Analysis
UN Sustainable Development Goals Color Wheel
UN Sustainable Development Goal Categories
Sources: Web Of Science, NC State University Libraries
Added: October 23, 2023

2021 article

Maximum gap in cyclotomic polynomials

Al-Kateeb, A., Ambrosino, M., Hong, H., & Lee, E. (2021, May 31). Journal of Number Theory, Vol. 12.

By: A. Al-Kateeb *, M. Ambrosino n, H. Hong n  & E. Lee *

author keywords: Cyclotomic polynomials; Inverse cyclotomic polynomials; Maximum gap
topics (OpenAlex): Coding theory and cryptography; Analytic Number Theory Research; Cryptography and Residue Arithmetic
Sources: Web Of Science, NC State University Libraries
Added: August 30, 2021

2020 article

A condition for multiplicity structure of univariate polynomials

Hong, H., & Yang, J. (2020, August 26). Journal of Symbolic Computation, Vol. 5, p. 15.

By: H. Hong n  & J. Yang *

author keywords: Parametric polynomial; Complex roots; Multiplicity structure; Discriminant; Resultant
topics (OpenAlex): Polynomial and algebraic computation; Advanced Differential Equations and Dynamical Systems; Coding theory and cryptography
TL;DR: This paper gives a novel condition for a univariate polynomial having a given multiplicity structure when the number of distinct roots is given and it is shown that the number and degree of polynomials in the condition are optimal. (via Semantic Scholar)
Source: ORCID
Added: November 6, 2020

2020 article

Global Identifiability of Differential Models

Hong, H., Ovchinnikov, A., Pogudin, G., & Yap, C. (2020, June 17). Communications on Pure and Applied Mathematics, Vol. 73, pp. 1831–1879.

By: H. Hong n , A. Ovchinnikov*, G. Pogudin* & C. Yap*

topics (OpenAlex): Polynomial and algebraic computation; Advanced Control Systems Optimization; Numerical methods for differential equations; Control Systems and Identification; Model Reduction and Neural Networks; Formal Methods in Verification
TL;DR: First, an algebraic criterion for global identifiability is rigorously derived, which yields a deterministic algorithm, which improves the efficiency by randomizing the algorithm while guaranteeing the probability of correctness. (via Semantic Scholar)
UN Sustainable Development Goals Color Wheel
UN Sustainable Development Goal Categories
Sources: Web Of Science, ORCID, NC State University Libraries
Added: July 6, 2020

2019 article

SIAN

Hong, H., Ovchinnikov, A., Pogudin, G., & Yap, C. (2019, November 8). ACM Communications in Computer Algebra, Vol. 53, pp. 37–40.

By: H. Hong n , A. Ovchinnikov*, G. Pogudin * & C. Yap *

topics (OpenAlex): Advanced Control Systems Optimization; Simulation Techniques and Applications; Fuzzy Logic and Control Systems
TL;DR: New software SIAN (Structural Identifiability ANalyser) that solves the problem of multiple parameter values that yield the same observed behavior even in the case of continuous noise-free data. (via Semantic Scholar)
UN Sustainable Development Goals Color Wheel
UN Sustainable Development Goal Categories
Sources: Web Of Science, ORCID, NC State University Libraries
Added: December 2, 2019

2018 article

Computer Algebra in Scientific Computing

Gerdt, V. P. 1947-, Koepf, W. 1953-, Seiler, W. M., & Vorožcov, E. V. 1946-. (2018, January 1). (V. P. Gerdt, W. Koepf, W. M. Seiler, & E. V. Vorozhtsov, Eds.). Lecture Notes in Computer Science, Vol. 11077, pp. 238–253.

By: V. Gerdt *, W. Koepf*, W. Seiler * & E. Vorožcov *

Ed(s): V. Gerdt *, W. Koepf*, W. Seiler * & E. Vorozhtsov *

topics (OpenAlex): Logic, programming, and type systems; Polynomial and algebraic computation; Computability, Logic, AI Algorithms
Source: ORCID
Added: November 6, 2020

2018 article

Locating and Counting Equilibria of the Kuramoto Model with Rank-One Coupling

Coss, O., Hauenstein, J. D., Hong, H., & Molzahn, D. K. (2018, January 1). SIAM Journal on Applied Algebra and Geometry, Vol. 2, pp. 45–71.

By: O. Coss, J. Hauenstein, H. Hong*  & D. Molzahn

author keywords: Kuramoto model; equilibria; univariate solving; homotopy continuation; numerical algebraic geometry
topics (OpenAlex): Nonlinear Dynamics and Pattern Formation; Slime Mold and Myxomycetes Research; Cellular Automata and Applications
TL;DR: An algorithm to locate only the real solutions of the Kuramoto model, thereby shortening computation time by several orders of magnitude in certain situations and conjecture an upper bound on the maximum number of equilibria for any number of oscillators which generalizes the known cases and is obtained on a range of explicitly provided natural frequencies. (via Semantic Scholar)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018

2018 article

Number of common roots and resultant of two tropical univariate polynomials

Hong, H., & Sendra, J. R. (2018, July 2). Journal of Algebra, Vol. 511, pp. 420–439.

By: H. Hong n  & J. Sendra *

author keywords: Tropical semifield; Tropical resultant; Common roots
topics (OpenAlex): Polynomial and algebraic computation; Algebraic Geometry and Number Theory; Nonlinear Waves and Solitons
Sources: Web Of Science, ORCID, NC State University Libraries
Added: October 19, 2018

2018 article

SIAN: software for structural identifiability analysis of ODE models

Hong, H., Ovchinnikov, A., Pogudin, G., & Yap, C. (2018, December 28). (J. Wren, Ed.). Bioinformatics, Vol. 35, pp. 2873–2874.

By: H. Hong n , A. Ovchinnikov*, G. Pogudin * & C. Yap *

Ed(s): J. Wren

MeSH headings : Models, Biological; Software
topics (OpenAlex): Real-time simulation and control systems; Advanced Control Systems Optimization; Fault Detection and Control Systems
TL;DR: A new software SIAN (Structural Identifiability ANalyser) that can tackle problems that could not be tackled by previously developed packages is presented. (via Semantic Scholar)
UN Sustainable Development Goals Color Wheel
UN Sustainable Development Goal Categories
Sources: Web Of Science, ORCID, NC State University Libraries
Added: October 28, 2019

2017 article

Improving root separation bounds

Herman, A., Hong, H., & Tsigaridas, E. (2017, March 23). Journal of Symbolic Computation, Vol. 84, pp. 25–56.

By: A. Herman n, H. Hong n  & E. Tsigaridas *

author keywords: Root separation bounds; Polynomial roots; Polynomial systems
topics (OpenAlex): Polynomial and algebraic computation; Numerical Methods and Algorithms; Advanced Numerical Analysis Techniques
TL;DR: Two new root separation bounds are presented: one univariate bound, and one multivariate bound that are not harder to compute than the previous bounds. (via Semantic Scholar)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018

2016 article

Algorithm for computing μ-bases of univariate polynomials

Hong, H., Hough, Z., & Kogan, I. A. (2016, September 19). Journal of Symbolic Computation, Vol. 80, pp. 844–874.

By: H. Hong n , Z. Hough n & I. Kogan n 

Contributors: H. Hong n , Z. Hough n & I. Kogan n 

author keywords: mu-basis; Syzygy module; Polynomial vectors; Rational curves
topics (OpenAlex): Polynomial and algebraic computation; Coding theory and cryptography; Cryptography and Residue Arithmetic
TL;DR: A new algorithm for computing a $\mu$-basis of the syzygy module of $n$ polynomials in one variable over an arbitrary field $\mathbb{K}$, based on standard linear algebra and completely self-contained is presented. (via Semantic Scholar)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018

2016 article

Open weak CAD and its applications

Han, J., Dai, L., Hong, H., & Xia, B. (2016, August 5). Journal of Symbolic Computation, Vol. 80, pp. 785–816.

By: J. Han *, L. Dai *, H. Hong n  & B. Xia *

author keywords: Open weak CAD; Open weak delineable; CAD projection; Semi-definiteness; Copositivity
topics (OpenAlex): Advanced Numerical Analysis Techniques; Polynomial and algebraic computation; Computational Geometry and Mesh Generation
TL;DR: An algorithm for computing projection polynomials of open weak CADs is proposed to compute the intersection of projection factor sets produced by different projection orders, which significantly improves the efficiency of solving copositive problems. (via Semantic Scholar)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018

2016 article

Resultants over commutative idempotent semirings I: Algebraic aspect

Hong, H., Kim, Y., Scholten, G., & Sendra, J. R. (2016, February 11). Journal of Symbolic Computation, Vol. 79, pp. 285–308.

By: H. Hong n , Y. Kim *, G. Scholten n & J. Sendra *

author keywords: Resultant; Commutative idempotent semiring; Tropical algebra; Sylvester matrix; Permanent
topics (OpenAlex): Polynomial and algebraic computation; Commutative Algebra and Its Applications; Advanced Numerical Analysis Techniques
TL;DR: It is proved that the same property of the resultant (with subtraction replaced with addition) holds over an arbitrary commutative idempotent semiring. (via Semantic Scholar)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018

2015 article

Explicit formula for optimal ate pairing over cyclotomic family of elliptic curves

Hong, H., Lee, E., & Lee, H.-S. (2015, January 30). Finite Fields and Their Applications, Vol. 34, pp. 45–74.

By: H. Hong n , E. Lee * & H. Lee *

author keywords: Pairing-based cryptosystem; Elliptic curve; Cyclotomic polynomial
topics (OpenAlex): Cryptography and Residue Arithmetic; Coding theory and cryptography; Cryptographic Implementations and Security
TL;DR: This work provides an explicit formula for vectors of polynomials describing optimal pairings over cyclotomic family of elliptic curves by partitioning a certain Cyclotomic polynomial. (via Semantic Scholar)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018

2015 article

On using Lazard's projection in CAD construction

McCallum, S., & Hong, H. (2015, March 14). Journal of Symbolic Computation, Vol. 72, pp. 65–81.

By: S. McCallum * & H. Hong n 

author keywords: Cylindrical algebraic decomposition; Projection operation; Theorem of Abhyankar and Jung
topics (OpenAlex): Advanced Numerical Analysis Techniques; Polynomial and algebraic computation; Numerical Methods and Algorithms
TL;DR: It is shown that Lazard's projection is valid for CAD construction for so-called well-oriented polynomial sets, however his notion of valuation does not make use of it. (via Semantic Scholar)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018

2015 article

Quality of positive root bounds

Herman, A., & Hong, H. (2015, October 2). Journal of Symbolic Computation, Vol. 74, pp. 592–602.

By: A. Herman n & H. Hong n 

author keywords: Polynomial roots; Positive root bounds; Absolute positiveness
topics (OpenAlex): Polynomial and algebraic computation; Mathematical functions and polynomials; Advanced Optimization Algorithms Research
TL;DR: The quality of positive root bounds is studied to find out whether the relative over-estimation of a positive root bound due to Hong is at most linear in the degree, no matter what the coefficient size is. (via Semantic Scholar)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018

2015 article

Real quantifier elimination for the synthesis of optimal numerical algorithms (Case study: Square root computation)

Eraşcu, M., & Hong, H. (2015, November 5). Journal of Symbolic Computation, Vol. 75, pp. 110–126.

By: M. Eraşcu * & H. Hong n 

author keywords: Synthesis; Optimal quadratically convergent algorithm; Square root; Real quantifier elimination
topics (OpenAlex): Numerical Methods and Algorithms; Polynomial and algebraic computation; Advanced Optimization Algorithms Research
TL;DR: This work overcame the difficulty of carefully reducing a complicated quantified formula into several simpler ones and automatically eliminating the quantifiers from the resulting ones using the state-of-the-art quantifier elimination software to synthesize semi-automatically an optimal quadratically1 convergent map, which is better than the well known hand-crafted Secant-Newton map. (via Semantic Scholar)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018

2014 article

An algebraic method for constructing stable and consistent autoregressive filters

Harlim, J., Hong, H., & Robbins, J. L. (2014, December 9). Journal of Computational Physics, Vol. 283, pp. 241–257.

By: J. Harlim*, H. Hong n  & J. Robbins n

author keywords: Autoregressive filter; Kalman filter; Parameter estimation; Model error
topics (OpenAlex): Meteorological Phenomena and Simulations; Climate variability and models; Wind and Air Flow Studies
TL;DR: An algebraic method to construct stable and consistent univariate autoregressive (AR) models of low order for filtering and predicting nonlinear turbulent signals with memory depth finds that the proposed AR models produce significantly more accurate short-term predictive skill and comparable filtering skill relative to the linear regression-based AR models. (via Semantic Scholar)
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UN Sustainable Development Goal Categories
13. Climate Action (Web of Science)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018

2014 chapter

ImUp: A Maple Package for Uniformity-Improved Reparameterization of Plane Curves

In Computer Mathematics (Vol. 10, pp. 437–451).

By: J. Yang *, D. Wang * & H. Hong n 

topics (OpenAlex): Advanced Numerical Analysis Techniques; Image Processing and 3D Reconstruction; Computer Graphics and Visualization Techniques
TL;DR: It is shown that the quality of plots of plane curves may be effectively improved by means of reparameterization using ImUp, and the capability and performance of the public functions of ImUp are illustrated. (via Semantic Scholar)
Sources: Crossref, ORCID, NC State University Libraries
Added: February 24, 2020

2014 article

Mathematical Software – ICMS 2014

Hong, H., & Yap, C. (2014, January 1). (H. Hong & C. Yap, Eds.). Lecture Notes in Computer Science, Vol. 8592.

By: H. Hong n  & C. Yap *

Ed(s): H. Hong n  & C. Yap *

topics (OpenAlex): Distributed and Parallel Computing Systems; Optimization and Search Problems
TL;DR: This talk illustrates the evolution of mathematics towards higher and higher levels of automation of its own problem solving and thinking process by a couple of examples of increasing sophistication starting from calculation with Roman numbers up to the automatic invention of algorithms like the speaker’s algorithm for computing Gröbner bases. (via Semantic Scholar)
Source: ORCID
Added: November 6, 2020

2014 book

Mathematical software - ICMS 2014: 4th International Congress, Seoul, South Korea, August 5-9, 2014 : Proceedings

Heidelberg: Springer.

Hoon Hong

Ed(s): H. Hong  & C. Yap

Source: NC State University Libraries
Added: August 6, 2018

2014 chapter

Pairing Inversion via Non-degenerate Auxiliary Pairings

In Pairing-Based Cryptography – Pairing 2013 (pp. 77–96).

By: S. Chang*, H. Hong n , E. Lee * & H. Lee *

topics (OpenAlex): Cryptography and Data Security; Cryptography and Residue Arithmetic; Coding theory and cryptography
TL;DR: This paper provides a simpler approach for PI by generalizing and simplifying Kanayama-Okamoto's approach, and defines an infinite set of curve parameters, which includes those of typical pairing friendly curves, and shows that PI of arbitrarily given generalized ate pairing can be reduced to modified EI in polynomial time. (via Semantic Scholar)
Sources: Crossref, NC State University Libraries
Added: February 24, 2020

2014 article

Pairing-Based Cryptography – Pairing 2013

Chang, S., Hong, H., Lee, E., & Lee, H.-S. (2014, January 1). (Z. Cao & F. Zhang, Eds.). Lecture Notes in Computer Science, Vol. 8365, pp. 77–96.

By: S. Chang, H. Hong , E. Lee & H. Lee

Ed(s): Z. Cao & F. Zhang

topics (OpenAlex): Coding theory and cryptography; Chaos-based Image/Signal Encryption
Source: ORCID
Added: November 6, 2020

2014 article

Special algorithm for stability analysis of multistable biological regulatory systems

Hong, H., Tang, X., & Xia, B. (2014, October 3). Journal of Symbolic Computation, Vol. 70, pp. 112–135.

By: H. Hong n , X. Tang  n & B. Xia *

author keywords: Quantifier elimination; Root classification; Biological regulation system; Stability
topics (OpenAlex): Advanced Control Systems Optimization; Receptor Mechanisms and Signaling; Gene Regulatory Network Analysis
TL;DR: A special algorithm is presented which is much more efficient than the general methods of solving the problem of counting (stable) equilibriums of an important family of algebraic differential equations modeling multistable biological regulatory systems. (via Semantic Scholar)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018

2014 article

Synthesis of optimal numerical algorithms using real quantifier elimination (case study: square root computation)

Eraşcu, M., & Hong, H. (2014, July 1). (K. Nabeshima, K. Nagasaka, F. Winkler, & Á. Szántó, Eds.). Proceedings of the 39th International Symposium on Symbolic and Algebraic Computation, pp. 162–169.

By: M. Eraşcu * & H. Hong n 

Ed(s): K. Nabeshima, K. Nagasaka, F. Winkler & Á. Szántó

topics (OpenAlex): Polynomial and algebraic computation; Numerical Methods and Algorithms; Digital Filter Design and Implementation
TL;DR: The on-going efforts to apply real quantifier elimination to the synthesis of optimal numerical algorithms were able to synthesize semi-automatically, under mild assumptions, a class of optimal maps, which are significantly better than the well known hand-crafted Secant-Newton map. (via Semantic Scholar)
Source: ORCID
Added: November 6, 2020

2013 article

A framework for improving uniformity of parameterizations of curves

Hong, H., Wang, D. M., & Yang, J. (2013, October 1). Science China Information Sciences, Vol. 56, pp. 1–22.

By: H. Hong n , D. Wang * & J. Yang *

author keywords: parametric curve; framework; quasi-speed; uniform parameterization; uniformity-improved reparameterization; optimal Mobius transformation
topics (OpenAlex): Advanced Numerical Analysis Techniques; Advanced Measurement and Metrology Techniques; Manufacturing Process and Optimization
TL;DR: A general framework is developed for studying uniformity behaviors under reparameterization via proper parameter transformation and for computingReparameterizations with improved uniformity of quasispeed by means of optimal single-piece, C0 piecewise, and C1 piecewise Möbius transformations. (via Semantic Scholar)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018

2013 chapter

Improving Angular Speed Uniformity by C 1 Piecewise Reparameterization

In Automated Deduction in Geometry (pp. 33–47).

By: J. Yang *, D. Wang * & H. Hong n 

topics (OpenAlex): Advanced Numerical Analysis Techniques; Advanced Vision and Imaging; Advanced Measurement and Metrology Techniques
TL;DR: A C 1 piecewise-rational reparameterization is shown that closely approximates to the arc-angle parameterization of any plane curve by C 1 pieceswise Mobius transformation by making use of the first derivative of the angular speed function. (via Semantic Scholar)
Sources: Crossref, ORCID, NC State University Libraries
Added: February 24, 2020

2013 article

Improving angular speed uniformity by reparameterization

Yang, J., Wang, D., & Hong, H. (2013, April 6). Computer Aided Geometric Design, Vol. 30, pp. 636–652.

By: J. Yang *, D. Wang * & H. Hong* 

topics (OpenAlex): Advanced Numerical Analysis Techniques; Polynomial and algebraic computation; Computer Graphics and Visualization Techniques
TL;DR: The notion of angular speed uniformity as a quality measure for parameter-izations of plane curves and an algorithm to compute uniform reparameterizations for quadratic and cubic curves are introduced and it is proved that only straight lines have uniform rational parameterizations. (via Semantic Scholar)
Sources: NC State University Libraries, ORCID, NC State University Libraries
Added: August 6, 2018

2013 article

Object-Image Correspondence for Algebraic Curves under Projections

Burdis, J. M., Kogan, I. A., & Hong, H. (2013, March 14). Symmetry Integrability and Geometry Methods and Applications, Vol. 3.

By: J. Burdis n, I. Kogan  & H. Hong 

Contributors: J. Burdis n, I. Kogan  & H. Hong 

author keywords: central and parallel projections; finite and affine cameras; camera decomposition; curves; classifying differential invariants; projective and affine transformations; signatures; machine vision
topics (OpenAlex): Advanced Numerical Analysis Techniques; Polynomial and algebraic computation; Advanced Vision and Imaging
UN Sustainable Development Goals Color Wheel
UN Sustainable Development Goal Categories
14. Life Below Water (Web of Science)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018

2013 journal article

Reducing Pairing Inversion to Exponentiation Inversion using Non-degenerate Auxiliary Pairing

IACR Cryptol. EPrint Arch., 2013, 313. http://eprint.iacr.org/2013/313

By: S. Chang, H. Hong , E. Lee & H. Lee

eprint.iacr.org
Source: ORCID
Added: November 6, 2020

2013 journal article

The Secant-Newton Map is Optimal Among Contracting Quadratic Maps for Square Root Computation

Reliab. Comput., 18, 73–81. http://interval.louisiana.edu/reliable-computing-journal/volume-18/reliable-computing-18-pp-073-081.pdf

By: M. Erascu & H. Hong 

interval.louisiana.edu
Source: ORCID
Added: November 6, 2020

2012 article

Computer Algebra in Scientific Computing

Yang, J., Wang, D., & Hong, H. (2012, January 1). (V. P. Gerdt, W. Koepf, E. W. Mayr, & E. V. Vorozhtsov, Eds.). Lecture Notes in Computer Science, Vol. 7442, pp. 349–360.

By: J. Yang, D. Wang & H. Hong 

Ed(s): V. Gerdt, W. Koepf, E. Mayr & E. Vorozhtsov

topics (OpenAlex): Advanced Database Systems and Queries
Source: ORCID
Added: November 6, 2020

2012 chapter

Improving Angular Speed Uniformity by Optimal C 0 Piecewise Reparameterization

In Computer Algebra in Scientific Computing (pp. 349–360).

By: J. Yang *, D. Wang * & H. Hong n 

topics (OpenAlex): Advanced Numerical Analysis Techniques; Advanced Vision and Imaging; Computer Graphics and Visualization Techniques
TL;DR: The C0 piecewise Mobius transformation is adapted to compute a C0 pieceswise-rational reparameterization of any plane curve that approximates to the arc-angle parameterization of the curve. (via Semantic Scholar)
Sources: Crossref, NC State University Libraries
Added: February 24, 2020

2012 article

Maximum gap in (inverse) cyclotomic polynomial

Hong, H., Lee, E., Lee, H.-S., & Park, C.-M. (2012, June 13). Journal of Number Theory, Vol. 132, pp. 2297–2315.

By: H. Hong n , E. Lee *, H. Lee * & C. Park*

author keywords: Cyclotomic polynomial; Inverse cyclotomic polynomial; Pairing-based cryptosystem
topics (OpenAlex): Coding theory and cryptography; Cryptography and Residue Arithmetic; Analytic Number Theory Research
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018

2012 article

Real solution formulas of cubic and quartic equations applied to generate dynamic diagrams with inequality constraints

Zhao, T., Hong, H., Wang, D., & Aubry, P. (2012, March 26). (S. Ossowski & P. Lecca, Eds.). Proceedings of the 27th Annual ACM Symposium on Applied Computing - SAC '12, pp. 94–101.

By: T. Zhao *, H. Hong n , D. Wang * & P. Aubry *

Ed(s): S. Ossowski & P. Lecca

topics (OpenAlex): Model-Driven Software Engineering Techniques; Constraint Satisfaction and Optimization; Data Management and Algorithms
TL;DR: It is shown that for generating dynamic diagrams automatically the performance of this approach can be enhanced, in terms of stability of numeric computation and quality of generated diagrams, when the used solution formulas of cubic and quartic equations are replaced by newly introduced real solution formulas with inequality constraints. (via Semantic Scholar)
Source: ORCID
Added: November 6, 2020

2012 article

Simple and exact formula for minimum loop length in Ate i pairing based on Brezing–Weng curves

Hong, H., Lee, E., Lee, H.-S., & Park, C.-M. (2012, January 21). Designs Codes and Cryptography, Vol. 67, pp. 271–292.

By: H. Hong n , E. Lee *, H. Lee * & C. Park*

author keywords: Pairing-based cryptosystem; Elliptic curves; Miller algorithm
topics (OpenAlex): Cryptography and Residue Arithmetic; Cryptographic Implementations and Security; Coding theory and cryptography
TL;DR: It will turn out that the formula depends only on essentially two parameters, providing freedom to choose the other parameters to address the design issues other than minimizing the loop length. (via Semantic Scholar)
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16. Peace, Justice and Strong Institutions (OpenAlex)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018

2011 article

Solution formulas for cubic equations without or with constraints

Zhao, T., Wang, D., & Hong, H. (2011, February 12). Journal of Symbolic Computation, Vol. 46, pp. 904–918.

By: T. Zhao *, D. Wang & H. Hong n 

author keywords: Cubic polynomial; Solution formula; Root convention; Constraint
topics (OpenAlex): Polynomial and algebraic computation; Mathematical and Theoretical Analysis; Advanced Topics in Algebra
TL;DR: A convention is presented (for square/cubic root) which provides correct interpretations of the Lagrange formula for all cubic polynomial equations with real coefficients under equality and inequality constraints. (via Semantic Scholar)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018

2011 article

Variant quantifier elimination

Hong, H., & Din, M. S. E. (2011, December 29). Journal of Symbolic Computation, Vol. 47, pp. 883–901.

By: H. Hong n  & M. Din *

topics (OpenAlex): Polynomial and algebraic computation; Formal Methods in Verification; Numerical Methods and Algorithms
TL;DR: The main idea underlying the algorithm is to substitute the repeated projection step of CAD by a single projection without carrying out a parametric existential decision over the reals, and it is found that the algorithm can tackle important and challenging problems, such as numerical stability analysis of the widely-used MacCormack's scheme. (via Semantic Scholar)
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16. Peace, Justice and Strong Institutions (OpenAlex)
Sources: NC State University Libraries, ORCID, NC State University Libraries
Added: August 6, 2018

2011 article

WTHD optimization for single phase multilevel converters with step modulation

Li, J., & Hong, H. (2011, November 1). IECON 2011 - 37th Annual Conference of the IEEE Industrial Electronics Society.

By: J. Li & H. Hong n 

topics (OpenAlex): Multilevel Inverters and Converters; Advanced DC-DC Converters; Silicon Carbide Semiconductor Technologies
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UN Sustainable Development Goal Categories
7. Affordable and Clean Energy (OpenAlex)
Source: ORCID
Added: November 6, 2020

2010 article

Connectivity in Semi-algebraic Sets

Hong, N. H. (2010, September 1). (T. Ida, V. Negru, T. Jebelean, D. Petcu, S. M. Watt, & D. Zaharie, Eds.). 2010 12th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing, pp. 4–7.

By: N. Hong n 

Ed(s): T. Ida, V. Negru, T. Jebelean, D. Petcu, S. Watt & D. Zaharie

author keywords: connectivity; road map; semi-algebraic sets; gradient fields; Morse-Smale complex
topics (OpenAlex): Polynomial and algebraic computation; Matrix Theory and Algorithms; Advanced Optimization Algorithms Research
Source: ORCID
Added: November 6, 2020

2009 article

Real-Time Algorithm for Minimizing THD in Multilevel Inverters With Unequal or Varying Voltage Steps Under Staircase Modulation

Liu, N. Y., Hong, N. H., & Huang, A. Q. (2009, February 26). IEEE Transactions on Industrial Electronics, Vol. 56, pp. 2249–2258.

By: N. Liu n, N. Hong n  & A. Huang n

author keywords: Multilevel inverter; multilevel pulsewidth modulation (PWM); power conversion; staircase modulation
topics (OpenAlex): Multilevel Inverters and Converters; Silicon Carbide Semiconductor Technologies; Microgrid Control and Optimization
TL;DR: A real-time algorithm for multilevel inverters with unequal or varying voltage steps under the staircase modulation results in the minimal total harmonic distortion of the output voltage of the inverter, which is proved by rigorous mathematical derivations in this paper. (via Semantic Scholar)
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Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018

2009 article

Real-Time Calculation of Switching Angles Minimizing THD for Multilevel Inverters With Step Modulation

Liu, N. Y., Hong, N. H., & Huang, A. Q. (2009, February 1). IEEE Transactions on Industrial Electronics, Vol. 56, pp. 285–293.

By: N. Liu  n, N. Hong n  & A. Huang n

author keywords: Multilevel inverter; optimal pulsewidth modulation (PWM); power conversion
topics (OpenAlex): Multilevel Inverters and Converters; Silicon Carbide Semiconductor Technologies; HVDC Systems and Fault Protection
TL;DR: A novel real-time algorithm for calculating switching angles that minimizes total harmonic distortion (THD) for step modulation is proposed and a mathematical proof that the output voltage has the minimum THD is given. (via Semantic Scholar)
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Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018

2009 journal article

Sylvester’s double sums: The general case

Journal of Symbolic Computation, 44(9), 1164–1175.

By: C. D’Andrea *, H. Hong n , T. Krick * & A. Szanto n 

author keywords: Subresultants; Double sums; Vandermonde determinants
topics (OpenAlex): History and Theory of Mathematics; Mathematical and Theoretical Analysis; Mathematics and Applications
TL;DR: The technique developed to answer the question of what are the other members of the Sylvester family turns out to be general enough to characterize allMembers of the family, providing a uniform method. (via Semantic Scholar)
Sources: Web Of Science, ORCID, NC State University Libraries, Crossref
Added: August 6, 2018

2009 article

Variant real quantifier elimination

Hong, H., & Din, M. S. E. (2009, July 28). (J. R. Johnson, H. Park, & E. Kaltofen, Eds.). Proceedings of the 2009 International Symposium on Symbolic and Algebraic Computation - ISSAC '09, pp. 183–190.

By: H. Hong n  & M. Din *

Ed(s): J. Johnson, H. Park & E. Kaltofen

topics (OpenAlex): Polynomial and algebraic computation; Formal Methods in Verification; Constraint Satisfaction and Optimization
TL;DR: The main idea underlying the algorithm VQE is to substitute the repeated projection step of CAD by a single projection without carrying out a parametric existential decision over the reals, which can tackle important and challenging problems, such as numerical stability analysis of the widely-used MacCormack's scheme. (via Semantic Scholar)
Source: ORCID
Added: November 6, 2020

2008 article

Are Buchberger's criteria necessary for the chain condition? (vol 42, pg 717, 2007)

Journal of Symbolic Computation, Vol. 43, pp. 233–233.

By: H. Hong  & J. Perry

Source: NC State University Libraries
Added: August 6, 2018

2008 article

Connectivity in semialgebraic sets (abstract only)

Quinn, R., & Hong, H. (2008, July 25). ACM Communications in Computer Algebra, Vol. 42, p. 86.

By: R. Quinn  n & H. Hong n 

topics (OpenAlex): Polynomial and algebraic computation; Numerical methods for differential equations; Advanced Optimization Algorithms Research
TL;DR: This talk considers the problem of deciding whether two given points in a semialgebraic set are connected, that is, whether the two points lie in the same connected component. (via Semantic Scholar)
Source: ORCID
Added: November 6, 2020

2007 journal article

Are Buchberger’s criteria necessary for the chain condition?

Journal of Symbolic Computation, 42(7), 717–732.

By: H. Hong n  & J. Perry*

author keywords: Grobner bases; S-polynomials; Buchberger criteria
topics (OpenAlex): Polynomial and algebraic computation; Advanced Numerical Analysis Techniques; Commutative Algebra and Its Applications
TL;DR: This paper has found an extension to Buchberger's criteria that is necessary as well as sufficient for skipping S-polynomial reductions, but not necessary when there are exactly three polynomials. (via Semantic Scholar)
Sources: Crossref, ORCID, NC State University Libraries
Added: August 28, 2020

2007 journal article

Corrigendum to “Are Buchberger’s criteria necessary for the chain condition?” [J. Symbolic Comput. 42 (2007) 717–732]

Journal of Symbolic Computation, 43(3), 233.

By: H. Hong n  & J. Perry*

topics (OpenAlex): Topological and Geometric Data Analysis
Sources: Crossref, NC State University Libraries
Added: August 28, 2020

2007 article

Foreword

Yap, C. K., & Hong, H. (2007, October 22). Mathematics in Computer Science, Vol. 1, pp. 3–7.

By: C. Yap * & H. Hong n 

topics (OpenAlex):
Source: ORCID
Added: November 6, 2020

2006 article

An elementary proof of Sylvester’s double sums for subresultants

Carlos, D. A., Hong, H., Krick, T., & Szanto, A. (2006, November 21). Journal of Symbolic Computation, Vol. 42, pp. 290–297.

By: D. Carlos *, H. Hong n , T. Krick * & A. Szanto n 

author keywords: subresultants; double-sum formula; Vandermonde determinant
topics (OpenAlex): Polynomial and algebraic computation; Mathematics and Applications; graph theory and CDMA systems
TL;DR: An elementary proof that uses only basic properties of matrix multiplication and Vandermonde determinants to express the polynomial subresultants in terms of the roots of the input polynomials is provided. (via Semantic Scholar)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018

2006 article

Automated Deduction in Geometry

Hong, H., & Wang, D. (2006, January 1). (H. Hong & D. Wang, Eds.). Lecture Notes in Computer Science, Vol. 3763.

By: H. Hong*  & D. Wang

Ed(s): H. Hong*  & D. Wang

topics (OpenAlex): Robotic Mechanisms and Dynamics; Manufacturing Process and Optimization; Mathematics, Computing, and Information Processing
Source: ORCID
Added: November 6, 2020

2006 chapter

Solving Dynamic Geometric Constraints Involving Inequalities

In J. Calmet, T. Ida, & D. Wang (Eds.), Artificial Intelligence and Symbolic Computation (pp. 181–195).

By: H. Hong n , L. Li *, T. Liang* & D. Wang *

Ed(s): J. Calmet, T. Ida & D. Wang *

topics (OpenAlex): Polynomial and algebraic computation; Formal Methods in Verification; Advanced Numerical Analysis Techniques
TL;DR: The method works by decomposing the system of constraints into finitely many explicit solution representations in terms of parameters with radicals using triangular decomposition and real quantifier elimination to solve dynamic geometric constraints involving equalities and inequalities. (via Semantic Scholar)
Sources: Crossref, ORCID, NC State University Libraries
Added: February 24, 2020

2005 article

Bruno Buchberger — A life devoted to symbolic computation

Hong, H., Kapur, D., Paule, P., & Winkler, F. (2005, October 13). Journal of Symbolic Computation, Vol. 41, pp. 255–258.

By: H. Hong n , D. Kapur *, P. Paule * & F. Winkler*

topics (OpenAlex): History and Theory of Mathematics
TL;DR: This special issue contains polished and refereed versions of many lectures presented at the symposium “LMCS 2002 – Logic, Mathematics and Computer Science: Interactions”, held in honor of Prof. Bruno Buchberger on the occasion of his 60th birthday in October 2002. (via Semantic Scholar)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018

2005 article

Non-linear real constraints in constraint logic programming

Hong, H. (2005, November 23). (H. Kirchner & G. Levi, Eds.). Lecture Notes in Computer Science, Vol. 632, pp. 201–212.

By: H. Hong* 

Ed(s): H. Kirchner & G. Levi

topics (OpenAlex): Logic, programming, and type systems; Formal Methods in Verification; Constraint Satisfaction and Optimization
TL;DR: This work reports the initial effort in tackling the problem with two methods developed in computer algebra during last three decades: Partial Cylindrical Algebraic Decomposition and Grobner basis to provide a full support of non-linear constraints over real numbers. (via Semantic Scholar)
Source: ORCID
Added: November 6, 2020

2005 article

The design of the SACLIB/PACLIB kernels

Hong, H., Neubacher, A., & Schreiner, W. (2005, November 23). (A. Miola, Ed.). Lecture Notes in Computer Science, Vol. 722, pp. 288–302.

By: H. Hong* , A. Neubacher* & W. Schreiner *

Ed(s): A. Miola

topics (OpenAlex): Parallel Computing and Optimization Techniques; Numerical Methods and Algorithms; Algorithms and Data Compression
Source: ORCID
Added: November 6, 2020

2003 article

Note on Jacobi’s method for approximating dominant roots

Hong, H. (2003, October 16). Journal of Symbolic Computation, Vol. 37, pp. 449–453.

By: H. Hong n 

author keywords: dominant roots; root bounds
topics (OpenAlex): Polynomial and algebraic computation; Numerical Methods and Algorithms; Iterative Methods for Nonlinear Equations
TL;DR: It is shown that Jacobi’s method can still be useful even when the dominant roots are not simple, if the authors use it for approximating the “distinct” dominant roots. (via Semantic Scholar)
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4. Quality Education (Web of Science)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018

2002 article

Sparse Resultant of Composed Polynomials I Mixed–Unmixed Case

Hong, H., & Minimair, M. (2002, April 1). Journal of Symbolic Computation, Vol. 33, pp. 447–465.

By: H. Hong n  & M. Minimair n

topics (OpenAlex): Polynomial and algebraic computation; Mathematical functions and polynomials; Matrix Theory and Algorithms
TL;DR: The main contribution of this paper is to provide an answer for the case when g1,…,gn are unmixed and the above expression can be applied to compute sparse resultants of composed polynomials with improved efficience. (via Semantic Scholar)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018

2001 article

Ore Principal Subresultant Coefficients in Solutions

Hong, H. (2001, February 1). Applicable Algebra in Engineering Communication and Computing, Vol. 11, pp. 227–237.

By: H. Hong n 

author keywords: ore polynomials; resultants; subresultants; elimination theory
topics (OpenAlex): Polynomial and algebraic computation; Advanced Optimization Algorithms Research; Numerical Methods and Algorithms
TL;DR: This expression can be viewed as a generalization of the well known expression for resultants of two commutative polynomials: the product of the pair-wise differences of their roots. (via Semantic Scholar)
Sources: ORCID, Web Of Science
Added: August 6, 2018

2001 article

Ore Subresultant Coefficients in Solutions

Hong, H. (2001, October 1). Applicable Algebra in Engineering Communication and Computing, Vol. 12, pp. 421–428.

By: H. Hong n 

author keywords: ore polynomials; resultants; subresultants
topics (OpenAlex): Numerical methods in inverse problems; Hydrocarbon exploration and reservoir analysis; Advanced Optimization Algorithms Research
TL;DR: This paper gives expressions for the principal (formal leading) coefficients of subresultants and all the other coefficients in terms of the solutions of Ore polynomials. (via Semantic Scholar)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018

2000 article

Editorial

Hong, H. (2000, January 1). Journal of Symbolic Computation, Vol. 29, pp. 3–4.

By: H. Hong* 

topics (OpenAlex):
Source: ORCID
Added: November 6, 2020

1998 article

Algorithms for Trigonometric Curves (Simplification, Implicitization, Parameterization)

Hong, H., & Schicho, J. (1998, September 1). Journal of Symbolic Computation, Vol. 26, pp. 279–300.

By: H. Hong n  & J. Schicho *

topics (OpenAlex): Advanced Numerical Analysis Techniques; Polynomial and algebraic computation; Cryptography and Residue Arithmetic
TL;DR: Algorithms for (a) simplifying a given parametric representation, (b) computing an implicit representation from a givenparametrically by a truncated Fourier series, and (c) computing a parametric representations from aGiven implicit representation are given. (via Semantic Scholar)
Sources: ORCID, Web Of Science
Added: August 6, 2018

1998 article

An Improvement of the Projection Operator in Cylindrical Algebraic Decomposition

Hong, H. (1998, January 1). Texts & Monographs in Symbolic Computation/Texts and Monographs in Symbolic Computation, pp. 166–173.

By: H. Hong* 

topics (OpenAlex): Polynomial and algebraic computation; Numerical Methods and Algorithms; Digital Filter Design and Implementation
Source: ORCID
Added: November 6, 2020

1998 article

Bounds for Absolute Positiveness of Multivariate Polynomials

Hong, H. (1998, May 1). Journal of Symbolic Computation, Vol. 25, pp. 571–585.

By: H. Hong* 

topics (OpenAlex): Polynomial and algebraic computation; Advanced Mathematical Theories and Applications; Mathematical functions and polynomials
TL;DR: A simple formula for computing bounds for the absolute positiveness of P, a multivariate polynomial with real coefficients, is provided and it is proved that the resulting bounds are guaranteed to be close to the optimal ones. (via Semantic Scholar)
Source: ORCID
Added: November 6, 2020

1998 conference paper

Computation of Variant Resultants

In B. F. Caviness & J. R. Johnson (Eds.), Quantifier Elimination and Cylindrical Algebraic Decomposition (pp. 327–340). Vienna: Springer Vienna.

By: H. Hong  & J. Sendra

Ed(s): B. Caviness & J. Johnson

Source: ORCID
Added: November 6, 2020

1998 article

Editorial

(1998, March 1). Mathematics and Computers in Simulation.

Hoon Hong

topics (OpenAlex):
Source: ORCID
Added: November 6, 2020

1998 article

Groebner Basis Under Composition I

Hong, H. (1998, May 1). Journal of Symbolic Computation, Vol. 25, pp. 643–663.

By: H. Hong* 

topics (OpenAlex): Polynomial and algebraic computation; Cryptography and Residue Arithmetic; Advanced Numerical Analysis Techniques
TL;DR: It is proved that this happens iff the composition is compatible with the term ordering and the nondivisibility of Groebner basis computation. (via Semantic Scholar)
Source: ORCID
Added: November 6, 2020

1998 article

Testing Positiveness of Polynomials

Hong, H., & Jakuš, D. (1998, August 1). Journal of Automated Reasoning, Vol. 21, pp. 23–38.

By: H. Hong n  & D. Jakuš*

author keywords: positiveness of polynomials; termination proofs; term rewrite systems
topics (OpenAlex): Polynomial and algebraic computation; Numerical Methods and Algorithms; Advanced Numerical Analysis Techniques
TL;DR: This paper exactly determines how partial several partial methods in the field of term rewriting systems are, and proposes simpler and/or more efficient methods with the same power. (via Semantic Scholar)
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16. Peace, Justice and Strong Institutions (OpenAlex)
Source: ORCID
Added: November 6, 2020

1997 journal article

Comparison of Several Decision Algorithms for the Existential Theory of the Reals

5.

By: H. Hong 

Source: ORCID
Added: November 6, 2020

1997 article

Heuristic search and pruning in polynomial constraints satisfaction

Hong, H. (1997, April 1). Annals of Mathematics and Artificial Intelligence, Vol. 19, pp. 319–334.

By: H. Hong* 

topics (OpenAlex): Polynomial and algebraic computation; Advanced Numerical Analysis Techniques; Cancer Treatment and Pharmacology
TL;DR: How certain AI techniques can be used to speed up an algebraic algorithm for deciding the satisfiability of a system of polynomial equations, dis-equations, and inequalities is reported. (via Semantic Scholar)
Source: ORCID
Added: November 6, 2020

1997 article

Implicitization of Nested Circular Curves

HONG, H. O. O. N. (1997, February 1). Journal of Symbolic Computation, Vol. 23, pp. 177–189.

By: H. Hong* 

topics (OpenAlex): Polynomial and algebraic computation; Advanced Numerical Analysis Techniques; Algebraic Geometry and Number Theory
TL;DR: This paper gives an efficient method for obtaining an implicit equation of a nested circular curve, a real plane curve traced by a point on a circle that rotates around another circle that again rotatesaround still another circle, and so on. (via Semantic Scholar)
Source: ORCID
Added: November 6, 2020

1997 journal article

Multivariate Resultants Under Composition

4.

By: H. Hong 

Source: ORCID
Added: November 6, 2020

1997 conference paper

Proceedings of the 2nd International Workshop on Parallel Symbolic Computation, PASCO 1997, July 20-22, 1997, Kihei, Hawaii, USA

ACM.

Hoon Hong

Ed(s): H. Hong , E. Kaltofen & M. Hitz

Source: ORCID
Added: November 6, 2020

1997 article

Special Issue on Application of Quantifier Elimination. Foreword of the Guest Editors

Hong, H., & Liska, R. (1997, August 1). Journal of Symbolic Computation, Vol. 24, p. 123.

By: H. Hong*  & R. Liska *

topics (OpenAlex): Advanced Algorithms and Applications; Advanced Computational Techniques and Applications
Source: ORCID
Added: November 6, 2020

1997 article

Subresultants Under Composition

Hong, H. (1997, April 1). Journal of Symbolic Computation, Vol. 23, pp. 355–365.

By: H. Hong* 

topics (OpenAlex): Advanced Combinatorial Mathematics; Polynomial and algebraic computation; Advanced Algebra and Logic
TL;DR: The main contribution of the paper is to show that the subresultants ``almost'' commute with composition, which generalizes the well-known fact that the resultant is invariant under translation. (via Semantic Scholar)
Source: ORCID
Added: November 6, 2020

1997 article

Testing Stability by Quantifier Elimination

HONG, H. O. O. N., LISKA, R. I. C. H. A. R. D., & STEINBERG, S. T. A. N. L. Y. (1997, August 1). Journal of Symbolic Computation, Vol. 24, pp. 161–187.

By: H. Hong* , R. Liska * & S. Steinberg*

topics (OpenAlex): Numerical Methods and Algorithms; Polynomial and algebraic computation; Modeling and Simulation Systems
TL;DR: This paper shows how to write all common stability problems as quantifier-elimination problems, and develops a set of computer-algebra tools that allows us to find analytic solutions to simple stability problems in a few seconds, and to solve some interesting problems in from a few minutes to a few hours. (via Semantic Scholar)
Source: ORCID
Added: November 6, 2020

1996 article

An efficient method for analyzing the topology of plane real algebraic curves

Hong, H. (1996, November 1). Mathematics and Computers in Simulation, Vol. 42, pp. 571–582.

By: H. Hong* 

author keywords: topology; algebraic curve; real roots; isolation; counting
topics (OpenAlex): Polynomial and algebraic computation; Numerical Methods and Algorithms; Advanced Numerical Analysis Techniques
TL;DR: A practically efficient algorithm for analyzing the topology of plane real algebraic curves is given, which produces a planar graph which is topologically equivalent to the real variety of the polynomial on the Euclidean plane. (via Semantic Scholar)
Source: ORCID
Added: November 6, 2020

1996 article

Groebner basis under composition II

Hong, H. (1996, January 1). (E. Engeler, B. F. Caviness, & Y. N. Lakshman, Eds.). Proceedings of the 1996 International Symposium on Symbolic and Algebraic Computation - ISSAC '96, pp. 79–85.

By: H. Hong* 

Ed(s): E. Engeler, B. Caviness & Y. Lakshman

topics (OpenAlex): Polynomial and algebraic computation; Logic, programming, and type systems; Commutative Algebra and Its Applications
TL;DR: It is proved that this happens i the composition is ‘compatible’ with the term ordering and the nondivisibility of Groebner basis computation. (via Semantic Scholar)
Source: ORCID
Added: November 6, 2020

1996 article

The exact region of stability for MacCormack scheme

Hong, H. (1996, December 1). Computing, Vol. 56, pp. 371–383.

By: H. Hong* 

author keywords: stability; MacCormack scheme; advection equation
topics (OpenAlex): Numerical methods for differential equations; Black Holes and Theoretical Physics; Nonlinear Waves and Solitons
TL;DR: It is proved that the stability region of the MacCormack scheme for this equation is exactly given. (via Semantic Scholar)
Source: ORCID
Added: November 6, 2020

1996 article

The exact stability region of the MacCormack scheme for the scalar advection equation

Hong, H. (1996, July 1). Applied Mathematics Letters, Vol. 9, pp. 99–101.

By: H. Hong* 

topics (OpenAlex): Navier-Stokes equation solutions; Computational Fluid Dynamics and Aerodynamics; Advanced Numerical Methods in Computational Mathematics
TL;DR: This note announces that the stability region of the MacCormack scheme for the scalar advection equation ut = aux + buy is exactly given by a Δt Δx 2 3 + b ΔT Δy 2 3 ≥ 1 where Δt, Δx and Δy are the grid distances. (via Semantic Scholar)
Source: ORCID
Added: November 6, 2020

1995 article

Applied Algebra, Algebraic Algorithms and Error-Correcting Codes

Hong, H. (1995, January 1). (G. D. Cohen, M. Giusti, & T. Mora, Eds.). Lecture Notes in Computer Science, Vol. 948, pp. 285–296.

By: H. Hong 

Ed(s): G. Cohen, M. Giusti & T. Mora

topics (OpenAlex): Coding theory and cryptography; Polynomial and algebraic computation
Source: ORCID
Added: November 6, 2020

1995 article

Bernstein form is inclusion monotone

Hong, H., & Stahl, V. (1995, March 1). Computing, Vol. 55, pp. 43–53.

By: H. Hong*  & V. Stahl*

author keywords: INTERVAL ANALYSIS; RANGE COMPUTATION; INCLUSION MONOTONICITY; BERNSTEIN COEFFICIENTS
topics (OpenAlex): Advanced Numerical Analysis Techniques; Advanced Optimization Algorithms Research; Advanced Control Systems Optimization
TL;DR: This paper shows that the bernstein form is inclusion monotone, i.e. the Bernstein Form inklusionsmonoton, which defines an interval extensionF off, which is called Bernstein form. (via Semantic Scholar)
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UN Sustainable Development Goal Categories
10. Reduced Inequalities (OpenAlex)
Source: ORCID
Added: November 6, 2020

1995 article

Preface

Hong, H., Wang, D., & Winkler, F. (1995, March 1). Annals of Mathematics and Artificial Intelligence, Vol. 13, pp. I-II.

By: H. Hong* , D. Wang * & F. Winkler*

topics (OpenAlex):
Source: ORCID
Added: November 6, 2020

1995 article

The Design of the SACLIB/PACLIB Kernels

Hong, H., Neubacher, A., & Schreiner, W. (1995, January 1). Journal of Symbolic Computation, Vol. 19, pp. 111–132.

By: H. Hong* , A. Neubacher* & W. Schreiner *

topics (OpenAlex): Parallel Computing and Optimization Techniques; Distributed and Parallel Computing Systems; Logic, programming, and type systems
TL;DR: The design of the kernels of two variants of the SAC-2 computer algebra library: Saclib and Paclib are described, supporting lightweight concurrency, non-determinism, and parallel garbage collection. (via Semantic Scholar)
Source: ORCID
Added: November 6, 2020

1994 article

Logic Programming and Automated Reasoning

Hong, H. (1994, January 1). (F. Pfenning, Ed.). Lecture Notes in Computer Science, Vol. 822, pp. 99–113.

By: H. Hong 

Ed(s): F. Pfenning

topics (OpenAlex): Logic, Reasoning, and Knowledge; Advanced Algebra and Logic; Semantic Web and Ontologies
Source: ORCID
Added: November 6, 2020

1994 article

Parallel Processing: CONPAR 94 — VAPP VI

Hong, H., & Loidl, H.-W. (1994, January 1). (B. Buchberger & J. Volkert, Eds.). Lecture Notes in Computer Science, Vol. 854, pp. 325–336.

By: H. Hong  & H. Loidl

Ed(s): B. Buchberger & J. Volkert

topics (OpenAlex):
Source: ORCID
Added: November 6, 2020

1994 article

Safe starting regions by fixed points and tightening

Hong, H., & Stahl, V. (1994, September 1). Computing, Vol. 53, pp. 323–335.

By: H. Hong*  & V. Stahl*

author keywords: NONLINEAR EQUATION SYSTEMS; INTERVAL ARITHMETIC; SAFE STARTING REGIONS; TIGHTENING
topics (OpenAlex): Numerical Methods and Algorithms; Polynomial and algebraic computation; Formal Methods in Verification
TL;DR: A method for finding safe starting regions for a given system of non-linear equations by enclosing the components of the equation system by univariante interval polynomials whose zero sets are found. (via Semantic Scholar)
Source: ORCID
Added: November 6, 2020

1993 conference paper

A New Library for Parallel Algebraic Computation

In R. F. Sincovec, D. E. Keyes, M. R. Leuze, L. R. Petzold, & D. A. Reed (Eds.), Proceedings of the Sixth SIAM Conference on Parallel Processing for Scientific Computing, PPSC 1993, Norfolk, Virginia, USA, March 22-24, 1993 (pp. 776–783). SIAM.

By: W. Schreiner & H. Hong 

Ed(s): R. Sincovec, D. Keyes, M. Leuze, L. Petzold & D. Reed

Source: ORCID
Added: November 6, 2020

1993 article

Applied Algebra, Algebraic Algorithms and Error-Correcting Codes

Cohen, G., & AAECC 1993 San Juan, P. R. (1993, January 1). (G. D. Cohen, T. Mora, & O. Moreno, Eds.). Lecture Notes in Computer Science, Vol. 673, pp. 170–179.

By: G. Cohen & P. AAECC 1993 San Juan

Ed(s): G. Cohen, T. Mora & O. Moreno

topics (OpenAlex): Coding theory and cryptography; Polynomial and algebraic computation
Source: ORCID
Added: November 6, 2020

1993 article

Artificial Intelligence and Symbolic Mathematical Computing

Hong, H. (1993, January 1). (J. Calmet & J. A. Campbell, Eds.). Lecture Notes in Computer Science, Vol. 737, pp. 152–165.

By: H. Hong 

Ed(s): J. Calmet & J. Campbell

topics (OpenAlex): Computability, Logic, AI Algorithms; Neural Networks and Applications; Data Mining Algorithms and Applications
Source: ORCID
Added: November 6, 2020

1993 article

Parallel Computation

Schreiner, W., & Hong, H. (1993, January 1). (J. Volkert, Ed.). Lecture Notes in Computer Science, Vol. 734, pp. 204–218.

By: W. Schreiner & H. Hong 

Ed(s): J. Volkert

topics (OpenAlex): Parallel Computing and Optimization Techniques; Computability, Logic, AI Algorithms
Source: ORCID
Added: November 6, 2020

1993 article

Quantifier Elimination for Formulas Constrained by Quadratic Equations via Slope Resultants

Hong, H. (1993, May 1). The Computer Journal, Vol. 36, pp. 439–449.

By: H. Hong* 

topics (OpenAlex): Polynomial and algebraic computation; Matrix Theory and Algorithms; Advanced Optimization Algorithms Research
TL;DR: An algorithm is given for eliminating the quantifier from a formula such that the system has no solution in R r and the output formulas are made of resultants and their variants, which the authors call slope resultants. (via Semantic Scholar)
Source: ORCID
Added: November 6, 2020

1993 article

Quantifier elimination for formulas constrained by quadratic equations

Hong, H. (1993, January 1). (M. Bronstein, Ed.). Proceedings of the 1993 International Symposium on Symbolic and Algebraic Computation - ISSAC '93, pp. 264–274.

By: H. Hong* 

Ed(s): M. Bronstein

topics (OpenAlex): Polynomial and algebraic computation; Numerical Methods and Algorithms; Formal Methods in Verification
TL;DR: An algorithm is given for constructing a quantifier free formula (a boolean expression of polynomial equations and inequalities) equivalent to a given formula of the form: (% c R)[azzz + alz + a. = O A F], where F is a quantifiers free formula in Z1, Z~, z, and az, al, ao are polynomials in z 1, Xr with real coefficients such that the system has no solution in Rr. (via Semantic Scholar)
Source: ORCID
Added: November 6, 2020

1993 chapter

RISC-CLP (Real): Logic Programming with Non-Linear Constraints over the Reals

In Constraint Logic Programming: Selected Research (pp. 133–159). Cambridge, MA, USA: MIT Press.

By: H. Hong 

Source: ORCID
Added: November 6, 2020

1993 article

Special Issue Editorial

Hong, H. (1993, May 1). The Computer Journal, Vol. 36, p. 399.

By: H. Hong* 

topics (OpenAlex):
Source: ORCID
Added: November 6, 2020

1992 article

Programming in PACLIB

Hong, H., & Schreiner, W. (1992, November 1). ACM SIGSAM Bulletin, Vol. 26, pp. 1–6.

By: H. Hong*  & W. Schreiner

topics (OpenAlex): Polynomial and algebraic computation; Tensor decomposition and applications; Parallel Computing and Optimization Techniques
TL;DR: This paper gives a short overview on PACLIB, a new system for parallel algebraic computation on shared memory computers that provides concurrency, shared memory communication, non-determinism, speculative parallelism, streams and pipelining and a parallelized garbage collection. (via Semantic Scholar)
Source: ORCID
Added: November 6, 2020

1992 article

Simple solution formula construction in cylindrical algebraic decomposition based quantifier elimination

Hong, H. (1992, January 1). (P. S. Wang, Ed.). Proceedings of the 1992 International Symposium on Symbolic and Algebraic Computation, ISSAC '92, Berkeley, CA, USA, July 27-29, 1992, pp. 177–188.

By: H. Hong* 

Ed(s): P. Wang* 

topics (OpenAlex): Polynomial and algebraic computation; Numerical Methods and Algorithms; Coding theory and cryptography
TL;DR: Since Tarski (1951) gave the first quantifier elimination algorithm for real closed fields, various improvements and new methods have been devised and analyzed. (via Semantic Scholar)
Source: ORCID
Added: November 6, 2020

1991 article

Partial Cylindrical Algebraic Decomposition for quantifier elimination

Collins, G. E., & Hong, H. (1991, September 1). Journal of Symbolic Computation, Vol. 12, pp. 299–328.

By: G. Collins* & H. Hong* 

topics (OpenAlex): Photonic and Optical Devices; Digital Filter Design and Implementation; Model Reduction and Neural Networks
TL;DR: This paper presents a method which intermingles CAD construction with truth evaluation so that parts of the CAD are constructed only as needed to further truth evaluation and aborts CAD construction as soon as no more truth evaluation is needed. (via Semantic Scholar)
Source: ORCID
Added: November 6, 2020

1990 article

An improvement of the projection operator in cylindrical algebraic decomposition

Hong, H. (1990, July 1). Proceedings of the International Symposium on Symbolic and Algebraic Computation - ISSAC '90.

By: H. Hong* 

topics (OpenAlex): Advanced Numerical Analysis Techniques; Polynomial and algebraic computation; Matrix Theory and Algorithms
TL;DR: By generalizing a lemma on which the proof of the original projection operation is based, this paper is able to find another projection operation which produces a smaller number of polynomials. (via Semantic Scholar)
Source: ORCID
Added: November 6, 2020

Employment

Updated: February 7th, 2026 15:18

North Carolina State University Raleigh, North Carolina, US
Professor Mathematics

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