Improvement of preconditioned bi-Lanczos-type algorithms with residual norm minimization for the stable solution of systems of linear equations

DOI10.1007/s13160-021-00480-0zbMath1481.65051OpenAlexW3198064550MaRDI QIDQ2070140

Shoji Itoh

Publication date: 21 January 2022

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

Full work available at URL: https://doi.org/10.1007/s13160-021-00480-0

zbMATH Keywords

changeover of stopping criterioncongruence of preconditioning conversiondirection of preconditioned systempreconditioned BiCGStabpreconditioned GPBiCG

Mathematics Subject Classification ID

Iterative numerical methods for linear systems (65F10) Preconditioners for iterative methods (65F08)

Uses Software

• SparseMatrix
• GpBiCg
• Lis

Cites Work

• GBi-CGSTAB(\(s,L\)): IDR(\(s\)) with higher-order stabilization polynomials
• BiCGstab(\(l\)) for linear equations involving unsymmetric matrices with complex spectrum
• Changing over stopping criterion for stable solving nonsymmetric linear equations by preconditioned conjugate gradient squared method
• Structure of the preconditioned system in various preconditioned conjugate gradient squared algorithms
• The university of Florida sparse matrix collection
• Interpreting IDR as a Petrov–Galerkin Method
• 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
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