Tensor-Krylov methods for large nonlinear equations
type: Item
instance of: scholarly article
title: Tensor-Krylov methods for large nonlinear equations
zbMATH Open document ID: 0853.65052
DOI: 10.1007/BF00248265
author: Ali Bouaricha
published in: Computational Optimization and Applications
publication date: 1996-07-01T00:00:00Z
review text: The author presents results on using iterative methods for the solution of the linear system which arises when using tensor methods for the solution of nonlinear equations. Tensor methods, originally proposed by \textit{R. B. Schnabel} and \textit{P. D. Frank} [SIAM J. Numer. Anal. 21, 815-843 (1984; Zbl 0562.65029)] are preferred to Newton methods when the Jacobian is ill-conditioned or singular at or near the solution. The author focuses on large systems with sparse Jacobian and reports numerical results on a number of difficult test problems which indicate that tensor methods are superior to Newton methods (both using Krylov-subspace-type iterative solvers for the linear equations) in most cases.
Mathematics Subject Classification ID: 65H10
Mathematics Subject Classification ID: 65F10
zbMATH DE Number: 894725
zbMATH Keywords: tensor-Krylov methods
zbMATH Keywords: Newton-Krylov methods
zbMATH Keywords: large systems of nonlinear equations
zbMATH Keywords: iterative methods
zbMATH Keywords: sparse Jacobian
zbMATH Keywords: numerical results
zbMATH Keywords: test problems
reviewed by: Claus Bendtsen
describes a project that uses: CGS
describes a project that uses: TENSOLVE
MaRDI profile type: Publication
cites work: Algorithm 768: TENSOLVE
cites work: Hybrid Krylov Methods for Nonlinear Systems of Equations
cites work: Q3702408
cites work: Local convergence analysis of tensor methods for nonlinear equations
cites work: Krylov Subspace Methods for Solving Large Unsymmetric Linear Systems
cites work: Conjugate Gradient-Like Algorithms for Solving Nonsymmetric Linear Systems
cites work: GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
cites work: Tensor Methods for Nonlinear Equations
cites work: A modular system of algorithms for unconstrained minimization
cites work: An Iterative Method for Nonsymmetric Systems with Multiple Right-Hand Sides
cites work: CGS, A Fast Lanczos-Type Solver for Nonsymmetric Linear systems
cites work: Bi-CGSTAB: A Fast and Smoothly Converging Variant of Bi-CG for the Solution of Nonsymmetric Linear Systems
full work available at URL: https://doi.org/10.1007/bf00248265
OpenAlex ID: W2028852110
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description: scientific article; zbMATH DE number 894725