A variant of the IDR\((s)\) method with the quasi-minimal residual strategy

DOI10.1016/j.cam.2011.07.027zbMath1300.65016OpenAlexW2005440992MaRDI QIDQ651884

Shao-Liang Zhang, Tomohiro Sogabe, Lei Du

Publication date: 19 December 2011

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.2011.07.027

zbMATH Keywords

linear systemsKrylov subspace methodsinduced dimension reduction IDR\((s)\)QMRQMRCGSTABQMRIDR\((s)\)

Mathematics Subject Classification ID

Iterative numerical methods for linear systems (65F10)

Related Items (6)

A quasi-minimal residual variant of IDRstab using the residual smoothing technique ⋮ A quasi-minimal residual variant of the BiCORSTAB method for nonsymmetric linear systems ⋮ Flexible and multi-shift induced dimension reduction algorithms for solving large sparse linear systems ⋮ IDR(\(s\)) for solving shifted nonsymmetric linear systems ⋮ An enhancement of the convergence of the IDR method ⋮ A shifted complex global Lanczos method and the quasi-minimal residual variant for the Stein-conjugate matrix equation \(X + A \overline{X} B = C\)

Uses Software

• SparseMatrix
• GpBiCg
• CGS

Cites Work

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• A block IDR\((s)\) method for nonsymmetric linear systems with multiple right-hand sides
• Bi-CGSTAB as an induced dimension reduction method
• GBi-CGSTAB(\(s,L\)): IDR(\(s\)) with higher-order stabilization polynomials
• IDR explained
• QMR: A quasi-minimal residual method for non-Hermitian linear systems
• BiCGstab(\(l\)) for linear equations involving unsymmetric matrices with complex spectrum
• Iterative solution of linear systems in the 20th century
• Eigenvalue Computations Based on IDR
• Algorithm 913
• Interpreting IDR as a Petrov–Galerkin Method
• Exploiting BiCGstab($\ell$) Strategies to Induce Dimension Reduction
• Recent computational developments in Krylov subspace methods for linear systems
• 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
• A Quasi-Minimal Residual Variant of the Bi-CGSTAB Algorithm for Nonsymmetric Systems
• GPBi-CG: Generalized Product-type Methods Based on Bi-CG for Solving Nonsymmetric Linear Systems
• Iterative Krylov Methods for Large Linear Systems
• A Transpose-Free Quasi-Minimal Residual Algorithm for Non-Hermitian Linear Systems
• Methods of conjugate gradients for solving linear systems

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