BiCR variants of the hybrid BiCG methods for solving linear systems with nonsymmetric matrices

DOI10.1016/j.cam.2009.03.003zbMath1189.65058OpenAlexW1985409333MaRDI QIDQ970386

Kuniyoshi Abe, Gerard L. G. Sleijpen

Publication date: 17 May 2010

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

Full work available at URL: https://doi.org/10.1016/j.cam.2009.03.003

zbMATH Keywords

convergencelinear systemsnumerical experimentsKrylov subspace methodrounding errorsnonsymmetric matricesbi-conjugate residual methodhybrid bi-conjugate gradient method

Mathematics Subject Classification ID

Iterative numerical methods for linear systems (65F10)

Related Items

Variants of the groupwise update strategy for short-recurrence Krylov subspace methods, BiCGCR2: A new extension of conjugate residual method for solving non-Hermitian linear systems, A quasi-minimal residual variant of the BiCORSTAB method for nonsymmetric linear systems, BiCR-type methods for families of shifted linear systems, Preconditioning complex symmetric linear systems, Converting BiCR method for linear equations with complex symmetric matrices, HOBi-CGSTAB and HOBi-CRSTAB methods for solving some tensor equations, A fast implicit difference scheme for a new class of time distributed-order and space fractional diffusion equations with variable coefficients, A new family of global methods for linear systems with multiple right-hand sides, Developing iterative algorithms to solve Sylvester tensor equations, A hybridized iterative algorithm of the BiCORSTAB and GPBiCOR methods for solving non-Hermitian linear systems, A novel class of block methods based on the blockAA^T-Lanczos bi-orthogonalization process for matrix equations

Uses Software

• MatrixMarket
• BiCGstab
• GpBiCg
• CGS

Cites Work

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• BiCGstab(\(l\)) and other hybrid Bi-CG methods
• Maintaining convergence properties of BiCGStab methods in finite precision arithmetic
• Generalized conjugate gradient squared
• The university of Florida sparse matrix collection
• Variational Iterative Methods for Nonsymmetric Systems of Linear Equations
• GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
• CGS, A Fast Lanczos-Type Solver for Nonsymmetric Linear systems
• Bi-CGSTAB: A Fast and Smoothly Converging Variant of Bi-CG for the Solution of Nonsymmetric Linear Systems
• Variants of BICGSTAB for Matrices with Complex Spectrum
• GPBi-CG: Generalized Product-type Methods Based on Bi-CG for Solving Nonsymmetric Linear Systems
• A Flexible Inner-Outer Preconditioned GMRES Algorithm