Verified Error Bounds for Isolated Singular Solutions of Polynomial Systems

DOI10.1137/120902914zbMath1310.65056arXiv1212.4699OpenAlexW2032671060MaRDI QIDQ2927825

No author found.

Publication date: 4 November 2014

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1212.4699

zbMATH Keywords

verificationalgorithmerror boundsquadratic convergenceNewton methoddeflationpolynomial systemsisolated singular solutionsmultiplicity structure

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Numerical computation of solutions to systems of equations (65H10) Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10) General theory of numerical methods in complex analysis (potential theory, etc.) (65E05) Algorithms with automatic result verification (65G20) Polynomials and rational functions of one complex variable (30C10) Numerical computation of roots of polynomial equations (65H04)

Related Items (14)

Inflation of poorly conditioned zeros of systems of analytic functions ⋮ On deflation and multiplicity structure ⋮ A heuristic method for certifying isolated zeros of polynomial systems ⋮ Efficient computation of dual space and directional multiplicity of an isolated point ⋮ Certifying solutions to overdetermined and singular polynomial systems over \(\mathbb{Q}\) ⋮ Verified inclusions for a nearest matrix of specified rank deficiency via a generalization of Wedin's \(\sin (\theta)\) theorem ⋮ A certified iterative method for isolated singular roots ⋮ VerifyRealRoots: a Matlab package for computing verified real solutions of polynomials systems of equations and inequalities ⋮ Numerical approximation of multiple isolated roots of analytical systems ⋮ A new deflation method for verifying the isolated singular zeros of polynomial systems ⋮ On isolation of simple multiple zeros and clusters of zeros of polynomial systems ⋮ Verified error bounds for singular solutions of nonlinear systems ⋮ An improved verification algorithm for nonlinear systems of equations based on Krawczyk operator ⋮ Locating the closest singularity in a polynomial homotopy

Uses Software

• INTLAB

This page was built for publication: Verified Error Bounds for Isolated Singular Solutions of Polynomial Systems