Theoretical and numerical comparisons of GMRES and WZ-GMRES

DOI10.1016/S0898-1221(04)90127-7zbMath1071.65037MaRDI QIDQ1767852

Zhongxiao Jia, Guizhi Chen

Publication date: 8 March 2005

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

zbMATH Keywords

stabilityconvergencenumerical experimentsiterative methodsKrylov subspace methodGMRES methodcondition numbersArnoldi processfinite precisionnon-symmetric matrix

Mathematics Subject Classification ID

Iterative numerical methods for linear systems (65F10)

Related Items

GMRES implementations and residual smoothing techniques for solving ill-posed linear systems, GMRES algorithms over 35 years, Two new variants of the simpler block GMRES method with vector deflation and eigenvalue deflation for multiple linear systems, A flexible and adaptive simpler block GMRES with deflated restarting for linear systems with multiple right-hand sides, A digraph-based hexahedral meshing method for coupled quasi-polycubes, Some iterative approaches for Sylvester tensor equations. I: A tensor format of truncated loose simpler GMRES

Uses Software

• Harwell-Boeing sparse matrix collection

Cites Work

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• Numerical stability of GMRES
• Roundoff error analysis of algorithms based on Krylov subspace methods
• Least Squares Residuals and Minimal Residual Methods
• Implementation of the GMRES Method Using Householder Transformations
• GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
• Sparse matrix test problems
• The convergence of Krylov subspace methods for large unsymmetric linear systems
• GMRES/CR and Arnoldi/Lanczos as Matrix Approximation Problems
• Estimating the Attainable Accuracy of Recursively Computed Residual Methods
• A simpler GMRES
• Computable Convergence Bounds for GMRES
• A Theoretical Comparison of the Arnoldi and GMRES Algorithms