Updated: July 5th, 2023 15:44

2020 journal article

Smooth Points on Semi-algebraic Sets

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

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.

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).

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.

author keywords: Domain decomposition; Homotopy continuation; Differential equations; Multiple solutions; Numerical algebraic geometry

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)

UN Sustainable Development Goal Categories

3. Good Health and Well-being
(Web of Science)

Source: Web Of Science

Added: August 6, 2018

2014 journal article

Certification and the potential energy landscape

*JOURNAL OF CHEMICAL PHYSICS*, *140*(22).

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.

author keywords: Polynomial system; Computational algebraic geometry; Numerical computation; Homotopy continuation; Symbolic computation; Primary decomposition

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.

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.

Source: Web Of Science

Added: August 6, 2018

2013 journal article

Communication: Certifying the potential energy landscape

*JOURNAL OF CHEMICAL PHYSICS*, *138*(17).

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.

author keywords: border rank; matrix multiplication

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.

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.

author keywords: Numerical algebraic geometry; Polynomial system; Witness sets; Projections; Membership test; Numerical irreducible decomposition; Geometric genus; Luroth quartics

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).

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.

author keywords: Real algebraic geometry; Infinitesimal deformation; Homotopy; Numerical algebraic geometry; Polynomial system

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.

author keywords: 65H10; 68W30; 14Q99; witness set; generic point; homotopy continuation; numerical algebraic geometry; numerical irreducible decomposition; primary decomposition; algebraic set; algebraic variety; LLL

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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