Jonathan David Hauenstein

Works (15)

Updated: October 14th, 2024 09:58

2020 journal article

Smooth Points on Semi-algebraic Sets

ACM COMMUNICATIONS IN COMPUTER ALGEBRA, 54(3), 105–108.

By: K. Harris  n, J. Hauenstein* & A. Szanto n 

topics (OpenAlex): Nonlinear Dynamics and Pattern Formation; Mathematical Dynamics and Fractals; Advanced Differential Equations and Dynamical Systems
Source: Web Of Science
Added: April 12, 2021

2019 journal article

Computing complex and real tropical curves using monodromy

JOURNAL OF PURE AND APPLIED ALGEBRA, 223(12), 5232–5250.

By: D. Brake*, J. Hauenstein* & C. Vinzant n

topics (OpenAlex): Polynomial and algebraic computation; Advanced Numerical Analysis Techniques; Algebraic Geometry and Number Theory
TL;DR: Algorithms for computing the rays of a complex and real tropical curve defined by polynomials with constant coefficients based on homotopy continuation, monodromy loops, and Cauchy integrals are presented. (via Semantic Scholar)
Source: Web Of Science
Added: August 5, 2019

2014 chapter

A Note on Global Newton Iteration Over Archimedean and Non-Archimedean Fields

In Computer Algebra in Scientific Computing (Vol. 8660, pp. 202–217).

By: J. Hauenstein n, V. Pan * & A. Szanto n 

topics (OpenAlex): Polynomial and algebraic computation; Numerical Methods and Algorithms; Mathematical and Theoretical Analysis
Sources: NC State University Libraries, Crossref
Added: August 6, 2018

2014 journal article

A bootstrapping approach for computing multiple solutions of differential equations

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 258, 181–190.

By: W. Hao *, J. Hauenstein n, B. Hu * & A. Sommese*

author keywords: Domain decomposition; Homotopy continuation; Differential equations; Multiple solutions; Numerical algebraic geometry
topics (OpenAlex): Polynomial and algebraic computation; Numerical methods for differential equations; Numerical Methods and Algorithms
TL;DR: This work uses a homotopy continuation based method arising from domain decomposition to solve polynomial systems arising from subdomains and then uses homOTopy continuation to build solutions of the originalPolynomial system. (via Semantic Scholar)
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UN Sustainable Development Goal Categories
Source: Web Of Science
Added: August 6, 2018

2014 journal article

Certification and the potential energy landscape

JOURNAL OF CHEMICAL PHYSICS, 140(22).

By: D. Mehta n, J. Hauenstein n & D. Wales *

topics (OpenAlex): Quantum Mechanics and Applications; Quantum chaos and dynamical systems; Cosmology and Gravitation Theories
TL;DR: This report provides details of how Smale's α-theory can be used to certify numerically obtained stationary points of a potential energy landscape, providing a mathematical proof that the numerical approximation does indeed correspond to an actual stationary point, independent of the precision employed. (via Semantic Scholar)
UN Sustainable Development Goals Color Wheel
UN Sustainable Development Goal Categories
7. Affordable and Clean Energy (OpenAlex)
Source: Web Of Science
Added: August 6, 2018

2014 journal article

Comparison of probabilistic algorithms for analyzing the components of an affine algebraic variety

APPLIED MATHEMATICS AND COMPUTATION, 231, 619–633.

By: D. Bates *, W. Decker*, J. Hauenstein n, C. Peterson *, G. Pfister*, F. Schreyer *, A. Sommese*, C. Wampler *

author keywords: Polynomial system; Computational algebraic geometry; Numerical computation; Homotopy continuation; Symbolic computation; Primary decomposition
topics (OpenAlex): Polynomial and algebraic computation; Numerical Methods and Algorithms; Advanced Numerical Analysis Techniques
TL;DR: Two fundamentally different approaches to computing and representing the solutions of polynomial systems: numerical homotopy continuation and symbolic computation are compared. (via Semantic Scholar)
Source: Web Of Science
Added: August 6, 2018

2013 journal article

A homotopy method based on WENO schemes for solving steady state problems of hyperbolic conservation laws

Journal of Computational Physics, 250, 332–346.

By: W. Hao, J. Hauenstein*, C. Shu, A. Sommese, Z. Xu & Y. Zhang

topics (OpenAlex): Fluid Dynamics and Turbulent Flows; Flood Risk Assessment and Management; Plant Water Relations and Carbon Dynamics
UN Sustainable Development Goals Color Wheel
UN Sustainable Development Goal Categories
15. Life on Land (OpenAlex)
Source: NC State University Libraries
Added: August 6, 2018

2013 journal article

Cell decomposition of almost smooth real algebraic surfaces

NUMERICAL ALGORITHMS, 63(4), 645–678.

By: G. Besana*, S. Di Rocco *, J. Hauenstein n, A. Sommese* & C. Wampler *

author keywords: Algebraic surface; Algebraic curve; Cell decomposition; Numerical algebraic geometry; Homotopy; Polynomial system
topics (OpenAlex): Polynomial and algebraic computation; Advanced Numerical Analysis Techniques; Commutative Algebra and Its Applications
Source: Web Of Science
Added: August 6, 2018

2013 journal article

Communication: Certifying the potential energy landscape

JOURNAL OF CHEMICAL PHYSICS, 138(17).

By: D. Mehta *, J. Hauenstein n & D. Wales *

topics (OpenAlex): Advanced Chemical Physics Studies; Spectroscopy and Quantum Chemical Studies; Molecular spectroscopy and chirality
TL;DR: This work applies Smale's α-theory to stationary points, providing a certification serving as a mathematical proof that the numerical approximation does indeed correspond to an actual stationary point, independent of the precision employed. (via Semantic Scholar)
UN Sustainable Development Goals Color Wheel
UN Sustainable Development Goal Categories
7. Affordable and Clean Energy (OpenAlex)
Source: Web Of Science
Added: August 6, 2018

2013 journal article

Equations for Lower Bounds on Border Rank

EXPERIMENTAL MATHEMATICS, 22(4), 372–383.

By: J. Hauenstein n, C. Ikenmeyer * & J. Landsberg *

author keywords: border rank; matrix multiplication
topics (OpenAlex): Polynomial and algebraic computation; Tensor decomposition and applications; Algebraic Geometry and Number Theory
TL;DR: It is shown that these newly obtained polynomials do not vanish on the matrix multiplication operator M 2, which gives a new proof that the border rank of the multiplication of 2×2 matrices is seven. (via Semantic Scholar)
Source: Web Of Science
Added: August 6, 2018

2013 journal article

Isosingular Sets and Deflation

FOUNDATIONS OF COMPUTATIONAL MATHEMATICS, 13(3), 371–403.

By: J. Hauenstein n & C. Wampler *

author keywords: Irreducible algebraic set; Deflation; Deflation sequence; Multiplicity; Isosingular set; Isosingular point; Isosingular local dimension; Numerical algebraic geometry; Polynomial system; Witness point; Witness set; Local dimension
topics (OpenAlex): Polynomial and algebraic computation; Commutative Algebra and Its Applications; Advanced Numerical Analysis Techniques
Source: Web Of Science
Added: August 6, 2018

2013 journal article

Membership tests for images of algebraic sets by linear projections

APPLIED MATHEMATICS AND COMPUTATION, 219(12), 6809–6818.

By: J. Hauenstein n & A. Sommese*

author keywords: Numerical algebraic geometry; Polynomial system; Witness sets; Projections; Membership test; Numerical irreducible decomposition; Geometric genus; Luroth quartics
topics (OpenAlex): Polynomial and algebraic computation; Advanced Numerical Analysis Techniques; Algebraic Geometry and Number Theory
TL;DR: Membership tests for both the constructible algebraic set and the algebraicSet are described, including computing the codimension one components of the irreducible component of the solution set of a polynomial system. (via Semantic Scholar)
Source: Web Of Science
Added: August 6, 2018

2013 journal article

Numerical elimination and moduli space of vacua

JOURNAL OF HIGH ENERGY PHYSICS, (9).

By: J. Hauenstein n, Y. He * & D. Mehta *

author keywords: Supersymmetric gauge theory; Differential and Algebraic Geometry; Super-string Vacua; Solitons Monopoles and Instantons
topics (OpenAlex): Black Holes and Theoretical Physics; Nonlinear Waves and Solitons; Algebraic structures and combinatorial models
Source: Web Of Science
Added: August 6, 2018

2013 journal article

Numerically Computing Real Points on Algebraic Sets

ACTA APPLICANDAE MATHEMATICAE, 125(1), 105–119.

By: J. Hauenstein n

author keywords: Real algebraic geometry; Infinitesimal deformation; Homotopy; Numerical algebraic geometry; Polynomial system
topics (OpenAlex): Polynomial and algebraic computation; Numerical Methods and Algorithms; Advanced Differential Equations and Dynamical Systems
TL;DR: This article transforms an approach of Rouillier, Roy, and Safey El Din, which is based on a classical optimization approach of Seidenberg, to develop a homotopy based approach for computing at least one point on each connected component of a real algebraic set. (via Semantic Scholar)
Source: Web Of Science
Added: August 6, 2018

2013 journal article

Recovering Exact Results from Inexact Numerical Data in Algebraic Geometry

EXPERIMENTAL MATHEMATICS, 22(1), 38–50.

By: D. Bates *, J. Hauenstein n, T. McCoy*, C. Peterson * & A. Sommese*

author keywords: 65H10; 68W30; 14Q99; witness set; generic point; homotopy continuation; numerical algebraic geometry; numerical irreducible decomposition; primary decomposition; algebraic set; algebraic variety; LLL
topics (OpenAlex): Polynomial and algebraic computation; Advanced Numerical Analysis Techniques; Commutative Algebra and Its Applications
TL;DR: This article illustrates how lattice-reduction algorithms may take as input numerically approximated generic points on Z and effectively extract exact elements for each Pi. (via Semantic Scholar)
Source: Web Of Science
Added: August 6, 2018

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