On the stable implementation of the generalized minimal error method

DOI10.1016/S0377-0427(98)00113-7zbMath0929.65016OpenAlexW2118468743MaRDI QIDQ1298807

Rüdiger Weiss, Miroslav Rozložnik

Publication date: 22 August 1999

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0377-0427(98)00113-7

zbMATH Keywords

numerical examplesnumerical stabilityHouseholder transformationsnonsymmetric systemsKrylov subspace iterationgeneralized minimal error method

Mathematics Subject Classification ID

Iterative numerical methods for linear systems (65F10)

Related Items (2)

Special issue: Developments and trends in iterative methods for large systems of equations -- in memoriam Rüdiger Weiss. Minisymposium: 16th IMACS world congress, Lausanne, Switzerland, August 21--25, 2000 ⋮ A framework for generalized conjugate gradient methods -- with special emphasis on contributions by Rüdiger Weiß

Cites Work

• Preconditioning strategies for models of incompressible flow
• On conjugate gradient type methods and polynomial preconditioners for a class of complex non-Hermitian matrices
• Iterative algorithms for Gram-Schmidt orthogonalization
• QMR: A quasi-minimal residual method for non-Hermitian linear systems
• Implementations of the GMRES method
• Numerical behaviour of the modified Gram-Schmidt GMRES implementation
• Numerical stability of GMRES
• Residual smoothing and peak/plateau behavior in Krylov subspace methods
• Implementation of the GMRES Method Using Householder Transformations
• GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
• Bi-CGSTAB: A Fast and Smoothly Converging Variant of Bi-CG for the Solution of Nonsymmetric Linear Systems
• Changing the Norm in Conjugate Gradient Type Algorithms
• Solution of Sparse Indefinite Systems of Linear Equations
• Residual Smoothing Techniques for Iterative Methods
• Error-Minimizing Krylov Subspace Methods
• A simpler GMRES
• The method of minimum iterations with minimum errors for a system of linear algebraic equations with a symmetrical matrix
• The principle of minimized iterations in the solution of the matrix eigenvalue problem
• The N‐Step Iteration Procedures
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: On the stable implementation of the generalized minimal error method