Hybrid Bi-CG methods with a Bi-CG formulation closer to the IDR approach

DOI10.1016/j.amc.2012.04.049zbMath1280.65032OpenAlexW2135027114MaRDI QIDQ387455

Gerard L. G. Sleijpen, Kuniyoshi Abe

Publication date: 23 December 2013

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

Full work available at URL: https://doi.org/10.1016/j.amc.2012.04.049

zbMATH Keywords

convergencelinear systemsnumerical experimentsKrylov subspace methodbi-conjugate gradient stabilized methodconjugate gradient squared methodBi-CGgeneralized product-type methodhybrid Bi-CG methodinduced dimension reduction (IDR) methodLanczos-type method

Mathematics Subject Classification ID

Iterative numerical methods for linear systems (65F10)

Related Items (1)

Variants of the groupwise update strategy for short-recurrence Krylov subspace methods

Uses Software

• BiCGstab
• GpBiCg
• CGS

Cites Work

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• Bi-CGSTAB as an induced dimension reduction method
• On the QMR approach for iterative methods including coupled three-term recurrences for solving nonsymmetric linear systems
• BiCGstab(\(l\)) for linear equations involving unsymmetric matrices with complex spectrum
• Maintaining convergence properties of BiCGStab methods in finite precision arithmetic
• Generalized conjugate gradient squared
• Solving linear equations with a stabilized GPBiCG method
• Exploiting BiCGstab($\ell$) Strategies to Induce Dimension Reduction
• Variational Iterative Methods for Nonsymmetric Systems of Linear Equations
• IDR(s): A Family of Simple and Fast Algorithms for Solving Large 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
• A Transpose-Free Quasi-Minimal Residual Algorithm for Non-Hermitian Linear Systems

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