Certified predictor-corrector tracking for Newton homotopies

DOI10.1016/j.jsc.2015.07.001zbMath1329.65110OpenAlexW1041626685MaRDI QIDQ898257

Jonathan D. Hauenstein, Alan C. jun. Liddell

Publication date: 8 December 2015

Published in: Journal of Symbolic Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jsc.2015.07.001

zbMATH Keywords

numerical exampleNewton's methodhomotopy continuationpolynomial systemnumerical algebraic geometryEuler predictoralpha theorycertified trackingNewton corrections

Mathematics Subject Classification ID

Numerical computation of solutions to systems of equations (65H10) Global methods, including homotopy approaches to the numerical solution of nonlinear equations (65H20) Numerical computation of roots of polynomial equations (65H04)

Related Items (9)

Certifying solutions to overdetermined and singular polynomial systems over \(\mathbb{Q}\) ⋮ Tensor decomposition and homotopy continuation ⋮ Rigid continuation paths II. structured polynomial systems ⋮ Complexity of sparse polynomial solving: homotopy on toric varieties and the condition metric ⋮ Numerical algebraic geometry and semidefinite programming ⋮ Foreword. What is numerical algebraic geometry? ⋮ A lifted square formulation for certifiable Schubert calculus ⋮ Rigid continuation paths I. Quasilinear average complexity for solving polynomial systems ⋮ Computing complex and real tropical curves using monodromy

Uses Software

• HOM4PS
• PHCpack
• Bertini
• NAG4M2
• NumericalAlgebraicGeometry

Cites Work

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• Complexity of Bezout's theorem. V: Polynomial time
• Robust certified numerical homotopy tracking
• Real solutions to systems of polynomial equations and parameter continuation
• Numerical algebraic geometry
• Certified Numerical Homotopy Tracking
• Galois groups of Schubert problems via homotopy computation
• An a posteriori certification algorithm for Newton homotopies
• The fundamental theorem of algebra and complexity theory
• Complexity of Bezout's Theorem I: Geometric Aspects
• Algorithm 795

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