Implementations of the GMRES method

DOI10.1016/0010-4655(89)90168-9zbMath0798.65041OpenAlexW2010576123MaRDI QIDQ1330648

Homer F. Walker

Publication date: 21 July 1994

Published in: Computer Physics Communications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0010-4655(89)90168-9

zbMATH Keywords

GMRES methodcomputational resultsgeneralized minimal residual methodlarge nonsymmetric linear systemsimplementationsnumerical reliability and efficiency

Mathematics Subject Classification ID

Computational methods for sparse matrices (65F50) Iterative numerical methods for linear systems (65F10) Software, source code, etc. for problems pertaining to linear algebra (15-04)

Related Items

A framework for generalized conjugate gradient methods -- with special emphasis on contributions by Rüdiger Weiß ⋮ Numerical stability of GMRES ⋮ Gram-Schmidt orthogonalization: 100 years and more ⋮ An engineering approach to generalized conjugate gradient methods and beyond ⋮ A theoretical overview of Krylov subspace methods ⋮ Parallelizable restarted iterative methods for nonsymmetric linear systems. part I: Theory ⋮ GMRES algorithms over 35 years ⋮ On the stable implementation of the generalized minimal error method ⋮ Preconditioned iterative methods for sparse linear algebra problems arising in circuit simulation

Cites Work

• Unnamed Item
• Generalized conjugate directions
• Generalized conjugate-gradient acceleration of nonsymmetrizable iterative methods
• Implementation of the GMRES Method Using Householder Transformations
• GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
• Solution of Sparse Indefinite Systems of Linear Equations
• Reorthogonalization and Stable Algorithms for Updating the Gram-Schmidt QR Factorization

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