Optimal homotopy methods for solving nonlinear systems. I: Nonsingular homotopy paths
type: Item
instance of: scholarly article
title: Optimal homotopy methods for solving nonlinear systems. I: Nonsingular homotopy paths
zbMATH Open document ID: 0797.65045
DOI: 10.1007/BF01385766
author: V. Pereyra
published in: Numerische Mathematik
publication date: 1994-05-18T00:00:00Z
full work available at URL: https://eudml.org/doc/133749
review text: The authors prove that in solving systems of nonlinear equations, a homotopy with a given structure has a distance monotone path under some regular conditions. The so-called local straighten-up method and global straighten-up method, as well as an adaptive step-size control strategy, are developed to approximate the optimal homotopy.
Mathematics Subject Classification ID: 65H10
Mathematics Subject Classification ID: 65H20
zbMATH DE Number: 569172
zbMATH Keywords: distance monotone path
zbMATH Keywords: systems of nonlinear equations
zbMATH Keywords: straighten-up method
zbMATH Keywords: adaptive step-size control strategy
zbMATH Keywords: optimal homotopy
reviewed by: Zeke Wang
MaRDI profile type: Publication
cites work: The Homotopy Continuation Method: Numerically Implementable Topological Procedures
cites work: Simplicial and Continuation Methods for Approximating Fixed Points and Solutions to Systems of Equations
cites work: Finite dimensional approximation of nonlinear problems. III: Simple bifurcation points
cites work: Finding Zeroes of Maps: Homotopy Methods That are Constructive With Probability One
cites work: A simple application of the homotopy method to symmetric eigenvalue problems
cites work: A modified continuation method for the numerical solution of nonlinear two-point boundary value problems by shooting techniques
cites work: A Theorem on Homotopy Paths
cites work: Q3702407
cites work: Solving nonlinear equations by adaptive homotopy continuation
cites work: A Constructive Proof of the Brouwer Fixed-Point Theorem and Computational Results
cites work: Homotopy method for generalized eigenvalue problems \(Ax=\lambda Bx\)
cites work: The numerical treatment of non-trivial bifurcation points
cites work: The Newton-Kantorovich Theorem
cites work: A Unified Convergence Theory for a Class of Iterative Processes
cites work: Solution Fields of Nonlinear Equations and Continuation Methods
cites work: Numerical computation of periodic orbits that bifurcate from stationary solutions of ordinary differential equations
cites work: Solving spline-collocation approximations to nonlinear two-point boundary-value problems by a homotopy method
cites work: The Computation of Symmetry-Breaking Bifurcation Points
cites work: Q5674306
cites work: Q3990257
description: scientific article; zbMATH DE number 569172