Agnes Szanto

Works (35)

Updated: July 5th, 2023 15:56

2022 article

A certified iterative method for isolated singular roots

Mantzaflaris, A., Mourrain, B., & Szanto, A. (2022, August 4). Journal of Symbolic Computation.

By: A. Mantzaflaris *, B. Mourrain * & A. Szanto n 

author keywords: Polynomial equations; Isolated solution; Multiple root; Certification; Newton iteration; Deflation
topics (OpenAlex): Polynomial and algebraic computation; Advanced Numerical Analysis Techniques; Iterative Methods for Nonlinear Equations
Sources: Web Of Science, NC State University Libraries
Added: October 3, 2022

2022 article

Certified Hermite matrices from approximate roots

Akoglu, T. A., & Szanto, A. (2022, December 16). Journal of Symbolic Computation.

By: T. Akoglu * & A. Szanto n 

author keywords: Symbolic-numeric computation; Polynomial systems; Approximate roots; Hermite matrices; Certification
topics (OpenAlex): Polynomial and algebraic computation; Advanced Numerical Analysis Techniques; Commutative Algebra and Its Applications
Source: Web Of Science
Added: February 20, 2023

2022 article

Smooth points on semi-algebraic sets

Harris, K., Hauenstein, J. D., & Szanto, A. (2022, September 29). Journal of Symbolic Computation.

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

author keywords: Computational real algebraic geometry; Real smooth points; Real dimension; Polar varieties; Numerical algebraic geometry; Kuramoto model
topics (OpenAlex): Mathematical Dynamics and Fractals; Advanced Differential Equations and Dynamical Systems; Nonlinear Dynamics and Pattern Formation
TL;DR: A simple procedure based on computing the critical points of some well-chosen function that guarantees the computation of smooth points in each connected bounded component of a real atomic semi-algebraic set is presented. (via Semantic Scholar)
Source: Web Of Science
Added: October 31, 2022

2021 article

Correction to: Preface

Cohen, A., Dahmen, W., Munthe-Kaas, H., Sombra, M., & Szanto, A. (2021, October 19). Foundations of Computational Mathematics, Vol. 10.

By: A. Cohen *, W. Dahmen*, H. Munthe-Kaas *, M. Sombra * & A. Szanto n 

topics (OpenAlex): National Identity and Symbolism; Human auditory perception and evaluation; History and advancements in chemistry
Sources: Web Of Science, NC State University Libraries
Added: November 1, 2021

2020 article

Certified Hermite Matrices from Approximate Roots - Univariate Case

Akoglu, T. A., & Szanto, A. (2020, January 1). Lecture Notes in Computer Science, pp. 3–9.

By: T. Akoglu * & A. Szanto n 

topics (OpenAlex): Advanced Mathematical Theories and Applications; Advanced Numerical Analysis Techniques; Mathematics and Applications
TL;DR: This study describes a symbolic-numeric algorithm to construct a rational matrix, called Hermite matrix, from the approximate roots and certify that this matrix is the true Hermite matrices corresponding to the roots \(V({\mathcal I})\). (via Semantic Scholar)
Source: ORCID
Added: November 6, 2020

2020 conference paper

Certified Hermite Matrices from Approximate Roots - Univariate Case

Mathematical Aspects of Computer and Information Sciences, 3–9.

By: T. Ayyildiz Akoglu & A. Szanto 

Source: ORCID
Added: November 13, 2020

2020 article

Punctual Hilbert scheme and certified approximate singularities

Mantzaflaris, A., Mourrain, B., & Szanto, A. (2020, July 20). Proceedings of the 45th International Symposium on Symbolic and Algebraic Computation.

By: A. Mantzaflaris *, B. Mourrain * & A. Szanto n 

topics (OpenAlex): Polynomial and algebraic computation; Advanced Numerical Analysis Techniques; Numerical Methods and Algorithms
TL;DR: A new method to certify that a nearby polynomial system has a singular isolated root and it is found that some of its strata can be rationally parametrized and exploit these parametrizations in the certification. (via Semantic Scholar)
Source: ORCID
Added: November 6, 2020

2020 article

Smooth Points on Semi-algebraic Sets

(2020, February 11).

Agnes Szanto

Source: ORCID
Added: November 6, 2020

2020 article

Smooth points on semi-algebraic sets

Harris, K., Hauenstein, J. D., & Szanto, A. (2020, September 1). ACM Communications in Computer Algebra.

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 article

Subresultants of (x−α) and (x−β) , Jacobi polynomials and complexity

Bostan, A., Krick, T., Szanto, A., & Valdettaro, M. (2019, October 10). Journal of Symbolic Computation, Vol. 101, pp. 330–351.

By: A. Bostan *, T. Krick *, A. Szanto n  & M. Valdettaro*

author keywords: Subresultants; Algorithms; Complexity; Jacobi polynomials
topics (OpenAlex): Mathematical functions and polynomials; Advanced Mathematical Identities; Polynomial and algebraic computation
TL;DR: It is shown that the coefficients of the subresultants of ( x − α ) m and (x − β ) n with respect to the monomial basis can be computed in linear arithmetic complexity, which is faster than for arbitrary polynomials. (via Semantic Scholar)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: July 6, 2020

2018 article

Closed formula for univariate subresultants in multiple roots

D'Andrea, C., Krick, T., Szanto, A., & Valdettaro, M. (2018, December 11). Linear Algebra and Its Applications, Vol. 565, pp. 123–155.

By: C. D'Andrea *, T. Krick *, A. Szanto n  & M. Valdettaro*

author keywords: Subresultants; Exchange lemma; Formulas in roots; Schur functions
topics (OpenAlex): Polynomial and algebraic computation; Numerical Methods and Algorithms; Digital Filter Design and Implementation; Advanced Combinatorial Mathematics; Advanced Numerical Analysis Techniques
Sources: Web Of Science, ORCID, NC State University Libraries
Added: February 25, 2019

2018 article

Irredundant Triangular Decomposition

Pogudin, G., & Szanto, A. (2018, July 11). Proceedings of the 2018 ACM International Symposium on Symbolic and Algebraic Computation, pp. 311–318.

By: G. Pogudin* & A. Szanto n 

topics (OpenAlex): Polynomial and algebraic computation; Advanced Combinatorial Mathematics; Advanced Numerical Analysis Techniques
TL;DR: This paper gives an algorithm to compute an irredundant triangular decomposition of an arbitrary algebraic set W defined by a set of polynomials in C[x1, x2, ..., xn]; this algorithm is randomized, and the probability of success is analyzed. (via Semantic Scholar)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: February 25, 2019

2017 article

Certifying solutions to overdetermined and singular polynomial systems over Q

Akoglu, T. A., Hauenstein, J. D., & Szanto, A. (2017, March 24). Journal of Symbolic Computation, Vol. 84, pp. 147–171.

By: T. Akoglu  n, J. Hauenstein * & A. Szanto n 

author keywords: Overdetermined; Polynomial system; Singular solutions; Certification; Rational univariate representation; Isosingular deflation
topics (OpenAlex): Polynomial and algebraic computation; Formal Methods in Verification; Numerical Methods and Algorithms
TL;DR: This papercertifies that a given point is near an exact root of an overdetermined or singular polynomial system with rational coefficients, and uses hybrid symbolic-numeric methods to compute the exact "rational univariate representation" of a component of the input system from approximate roots. (via Semantic Scholar)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018

2017 journal article

Subresultants in multiple roots: An extremal case

Linear Algebra and Its Applications, 529, 185–198.

By: A. Bostan *, C. D'Andrea *, T. Krick *, A. Szanto n  & M. Valdettaro*

author keywords: Subresultants; Hankel matrices; Ostrowski's determinant; Pfaff-Saalschiltz identity
topics (OpenAlex): Polynomial and algebraic computation; Mathematical functions and polynomials; Nonlinear Waves and Solitons; Advanced Numerical Analysis Techniques
Sources: Crossref, ORCID, NC State University Libraries
Added: August 28, 2020

2016 article

On deflation and multiplicity structure

Hauenstein, J. D., Mourrain, B., & Szanto, A. (2016, November 14). Journal of Symbolic Computation, Vol. 83, pp. 228–253.

By: J. Hauenstein *, B. Mourrain * & A. Szanto n 

author keywords: Deflation; Multiplicity structure; Newton's method; Inverse system; Multiplication matrix
topics (OpenAlex): Polynomial and algebraic computation; Cancer Treatment and Pharmacology; Numerical methods for differential equations
TL;DR: Two new constructions related to singular solutions of polynomial systems are presented, one of which gives the coefficients of the so-called inverse system or dual basis, which defines the multiplicity structure at the singular root and the other allows one to treat all conjugate roots simultaneously. (via Semantic Scholar)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018

2016 article

Symmetric interpolation, Exchange Lemma and Sylvester sums

Krick, T., Szanto, A., & Valdettaro, M. (2016, October 19). Communications in Algebra, Vol. 45, pp. 3231–3250.

By: T. Krick *, A. Szanto n  & M. Valdettaro*

author keywords: Subresultants; Sylvester double sums; symmetric Lagrange interpolation
topics (OpenAlex): Advanced Numerical Analysis Techniques; Polynomial and algebraic computation; Mathematical functions and polynomials
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018

2015 article

Certifying Isolated Singular Points and their Multiplicity Structure

Hauenstein, J. D., Mourrain, B., & Szanto, A. (2015, June 24). Proceedings of the 2015 ACM on International Symposium on Symbolic and Algebraic Computation - ISSAC '15.

By: J. Hauenstein *, B. Mourrain * & A. Szanto n 

author keywords: isolated point; root deflation; dual space; multiplicity structure; inverse system; local algebra; multiplication operator
topics (OpenAlex): Polynomial and algebraic computation; Cancer Treatment and Pharmacology; Algebraic Geometry and Number Theory
TL;DR: Two new constructions related to singular solutions of polynomial systems are presented, one of which gives the coefficients of the so-called inverse system or dual basis, which defines the multiplicity structure at the singular root and the other presents a system of equations in the original variables plus a relatively small number of new variables. (via Semantic Scholar)
Source: ORCID
Added: November 6, 2020

2015 article

Special issue on the conference ISSAC 2014: Symbolic computation and computer algebra

Nagasaka, K., Szanto, A., & Winkler, F. (2015, November 5). Journal of Symbolic Computation, Vol. 75, pp. 1–3.

By: K. Nagasaka *, A. Szanto n  & F. Winkler*

topics (OpenAlex): Computability, Logic, AI Algorithms; Polynomial and algebraic computation; Cellular Automata and Applications
Sources: Web Of Science, NC State University Libraries
Added: August 6, 2018

2014 chapter

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

In Computer Algebra in Scientific Computing (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: Crossref, NC State University Libraries
Added: August 6, 2018

2014 conference paper

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

In V. P. Gerdt, W. Koepf, W. M. Seiler, & E. V. Vorozhtsov (Eds.), Computer Algebra in Scientific Computing (pp. 202–217). Cham: Springer International Publishing.

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

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

Event: at Cham

Source: ORCID
Added: November 6, 2020

2014 article

Overdetermined Weierstrass iteration and the nearest consistent system

Ruatta, O., Sciabica, M., & Szanto, A. (2014, November 11). Theoretical Computer Science, Vol. 562, pp. 346–364.

By: O. Ruatta*, M. Sciabica n & A. Szanto n 

author keywords: Approximate GCD; Overdetermined systems; Nearest consistent system; Weierstrass-Durand-Kerner method
topics (OpenAlex): Polynomial and algebraic computation; Advanced Optimization Algorithms Research; Advanced Numerical Analysis Techniques
TL;DR: A generalization of the Weierstrass iteration for overdetermined systems of equations and it is proved that the proposed method is the Gauss-Newton iteration to find the nearest system which has at least k common roots and which is obtained via a perturbation of prescribed structure. (via Semantic Scholar)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018

2014 article

Subresultants, Sylvester sums and the rational interpolation problem

D'Andrea, C., Krick, T., & Szanto, A. (2014, August 7). Journal of Symbolic Computation, Vol. 68, pp. 72–83.

By: C. D'Andrea *, T. Krick * & A. Szanto n 

author keywords: Rational interpolation; Cauchy interpolation; Osculatory interpolation; Rational Hermite interpolation; Subresultants; Sylvester sums
topics (OpenAlex): Advanced Numerical Analysis Techniques; Polynomial and algebraic computation; Mathematical functions and polynomials
TL;DR: A solution for the classical univariate rational interpolation problem by means of (univariate) subresultants is presented, giving explicit formulas for the solution in terms of symmetric functions of the input data, generalizing the well-known formulas for Lagrange interpolation. (via Semantic Scholar)
Sources: Web Of Science, NC State University Libraries
Added: August 6, 2018

2012 article

Subresultants in multiple roots

Bostan, A., D'Andrea, C., Krick, T., Szanto, A., & Valdettaro, M. (2012, December 8). Linear Algebra and Its Applications, Vol. 438, pp. 1969–1989.

By: A. Bostan, C. D'Andrea  n, T. Krick  n, A. Szanto n  & M. Valdettaro

author keywords: subresultants; Sylvester sums; root multiplicity; Hermite interpolation
topics (OpenAlex): Polynomial and algebraic computation; Advanced Numerical Analysis Techniques; Mathematics and Applications
Sources: Web Of Science, NC State University Libraries
Added: August 6, 2018

2012 article

Sylvester’s double sums: An inductive proof of the general case

Krick, T., & Szanto, A. (2012, January 30). Journal of Symbolic Computation.

By: T. Krick * & A. Szanto n 

author keywords: Sylvester's double sums; Subresultants
topics (OpenAlex): Advanced Mathematical Theories and Applications; Mathematics and Applications; graph theory and CDMA systems
TL;DR: It is shown how induction also allows to obtain the full description of Sylvester?s double-sums. (via Semantic Scholar)
Sources: Web Of Science, NC State University Libraries
Added: August 6, 2018

2011 journal article

On the computation of matrices of traces and radicals of ideals

Journal of Symbolic Computation, 47(1), 102–122.

By: I. Janovitz-Freireich*, B. Mourrain *, L. Rónyai * & Á. Szántó n 

author keywords: Matrix of traces; Radical of an ideal
topics (OpenAlex): Polynomial and algebraic computation; Commutative Algebra and Its Applications; Algebraic Geometry and Number Theory
TL;DR: Borders on the degrees needed for the Macaulay matrix are proved in the case when I has finitely many projective roots in P"K^m" and previous results which work only for the case where A is Gorenstein to the non-Gorenstein case are extended. (via Semantic Scholar)
Sources: Crossref, NC State University Libraries
Added: June 15, 2021

2011 chapter

Symbolic-Numeric Solution of Ill-Conditioned Polynomial Systems (Survey Talk Overview) (Invited Talk)

In V. P. Gerdt, W. Koepf, E. W. Mayr, & E. V. Vorozhtsov (Eds.), Computer Algebra in Scientific Computing (CASC 2011) (pp. 345–347).

By: A. Szanto n 

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

topics (OpenAlex): Polynomial and algebraic computation; Advanced Differential Equations and Dynamical Systems; Commutative Algebra and Its Applications
TL;DR: A family of iterative techniques which, for a given inexact system of polynomials and given root structure, computes the nearest system which has roots with the given structure are described. (via Semantic Scholar)
Sources: Crossref, NC State University Libraries
Added: June 15, 2021

2009 article

A bound for orders in differential Nullstellensatz

Golubitsky, O., Kondratieva, M., Ovchinnikov, A., & Szanto, A. (2009, June 28). Journal of Algebra, Vol. 322, pp. 3852–3877.

By: O. Golubitsky*, M. Kondratieva*, A. Ovchinnikov * & A. Szanto n 

author keywords: Differential algebra; Characteristic sets; Radical differential ideals; Differential Nullstellensatz
topics (OpenAlex): Polynomial and algebraic computation; Advanced Differential Equations and Dynamical Systems; Numerical methods for differential equations
Sources: Web Of Science, NC State University Libraries
Added: August 6, 2018

2009 article

Multivariate subresultants using Jouanolou matrices

Szanto, A. (2009, November 29). Journal of Pure and Applied Algebra, Vol. 214, pp. 1347–1369.

By: A. Szanto n 

topics (OpenAlex): Polynomial and algebraic computation; Advanced Fiber Laser Technologies; Commutative Algebra and Its Applications
Sources: Web Of Science, 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: Crossref, NC State University Libraries, Web Of Science, ORCID
Added: August 6, 2018

2008 article

Nearest multivariate system with given root multiplicities

Pope, S. R., & Szanto, A. (2008, October 5). Journal of Symbolic Computation, Vol. 44, pp. 606–625.

By: S. Pope n & A. Szanto n 

author keywords: Approximate polynomial systems; Multiple roots; Multiplicity structure; Weierstrass iteration
topics (OpenAlex): Polynomial and algebraic computation; Numerical Methods and Algorithms; Advanced Numerical Analysis Techniques
TL;DR: A symbolic-numeric technique to find the closest multivariate polynomial system to a given one which has roots with prescribed multiplicity structure and a simplified version of the iteration function analogously to the classical Weierstrass iteration, which allows a component-wise expression, and thus reduces the computational cost of each iteration. (via Semantic Scholar)
Sources: Web Of Science, NC State University Libraries
Added: August 6, 2018

2007 journal article

Approximate Radical for Clusters: A Global Approach Using Gaussian Elimination or SVD

Mathematics in Computer Science, 1(2), 393–425.

By: I. Janovitz-Freireich n, L. Rónyai * & Á. Szántó n 

author keywords: Radical ideal; clusters; matrix of traces; symbolic-numeric computation
topics (OpenAlex): Graph theory and applications; Matrix Theory and Algorithms; Polynomial and algebraic computation
TL;DR: A method based on Dickson’s lemma to compute the “approximate radical” of the matrix of traces, attached to a zero dimensional ideal which has zero clusters, is presented. (via Semantic Scholar)
Sources: Crossref, NC State University Libraries
Added: June 15, 2021

2007 article

Solving over-determined systems by the subresultant method (with an appendix by Marc Chardin)

Szanto, A. (2007, September 15). Journal of Symbolic Computation, Vol. 43, pp. 46–74.

By: A. Szanto n 

author keywords: multivariate subresultant; over-determined polynomial system; solution of polynomial system
topics (OpenAlex): Polynomial and algebraic computation; Commutative Algebra and Its Applications; Advanced Numerical Analysis Techniques
TL;DR: It is proved that certain previously known matrix constructions, in particular, Macaulay's, Chardin's and Jouanolou's resultant and sub resultant matrices possess the subresultant properties. (via Semantic Scholar)
Sources: Web Of Science, NC State University Libraries
Added: August 6, 2018

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

2006 journal article

Re: “Multivariate subresultants in roots” [J. Algebra 302 (2006) 16–36]

Journal of Algebra, 303(2), 449.

By: C. D'Andrea *, T. Krick * & A. Szanto n 

topics (OpenAlex): Polynomial and algebraic computation
Sources: Crossref, NC State University Libraries
Added: August 28, 2020

2005 article

Multivariate subresultants in roots

D'Andrea, C., Krick, T., & Szanto, A. (2005, November 3). Journal of Algebra, Vol. 302, pp. 16–36.

By: C. D'Andrea *, T. Krick * & A. Szanto n 

author keywords: subresultants; Poisson product formula; Vandermonde determinants
topics (OpenAlex): Polynomial and algebraic computation; Advanced Numerical Analysis Techniques; Mathematics and Applications
Sources: Web Of Science, NC State University Libraries
Added: August 6, 2018

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