A quasi-minimal residual variant of IDRstab using the residual smoothing technique

DOI10.1016/j.amc.2014.03.034zbMath1336.65035OpenAlexW1967092701MaRDI QIDQ273244

Kuniyoshi Abe, Emiko Ishiwata, Kensuke Aihara

Publication date: 21 April 2016

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

Full work available at URL: https://doi.org/10.1016/j.amc.2014.03.034

zbMATH Keywords

linear systemsIDRstab methodinduced dimension reductionquasi-minimal residualresidual smoothing technique

Mathematics Subject Classification ID

Iterative numerical methods for linear systems (65F10)

Related Items (1)

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

• CGS
• IDRStab
• Algorithm 913
• CIMGS

Cites Work

• Unnamed Item
• IDR: a new generation of Krylov subspace methods?
• Bi-CGSTAB as an induced dimension reduction method
• A variant of the IDR\((s)\) method with the quasi-minimal residual strategy
• GBi-CGSTAB(\(s,L\)): IDR(\(s\)) with higher-order stabilization polynomials
• Numerical study on incomplete orthogonal factorization preconditioners
• Modified incomplete orthogonal factorization methods using Givens rotations
• QMR: A quasi-minimal residual method for non-Hermitian linear systems
• BiCGstab(\(l\)) for linear equations involving unsymmetric matrices with complex spectrum
• A variant of IDRstab with reliable update strategies for solving sparse linear systems
• An alternative implementation of the IDRstab method saving vector updates
• Flexible and multi-shift induced dimension reduction algorithms for solving large sparse linear systems
• Algorithm 913
• Exploiting BiCGstab($\ell$) Strategies to Induce Dimension Reduction
• IDR(s): A Family of Simple and Fast Algorithms for Solving Large Nonsymmetric Systems of Linear Equations
• 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
• Residual Smoothing Techniques for Iterative Methods
• A Quasi-Minimal Residual Variant of the Bi-CGSTAB Algorithm for Nonsymmetric Systems
• CIMGS: An Incomplete Orthogonal FactorizationPreconditioner
• Hermitian and Skew-Hermitian Splitting Methods for Non-Hermitian Positive Definite Linear Systems
• Iterative Solution Methods
• A Transpose-Free Quasi-Minimal Residual Algorithm for Non-Hermitian Linear Systems
• A class of incomplete orthogonal factorization methods. I: Methods and theories
• Residual smoothing techniques: Do they improve the limiting accuracy of iterative solvers?

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