On the QMR approach for iterative methods including coupled three-term recurrences for solving nonsymmetric linear systems

DOI10.1016/S0168-9274(98)00004-XzbMath0939.65051OpenAlexW2021735926MaRDI QIDQ1294470

Zhi-Hao Cao

Publication date: 10 July 2000

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0168-9274(98)00004-x

zbMATH Keywords

iterative methodsnon-symmetric linear systemsbreakdown avoiding algorithmquasi-minimal residual algorithmsthree-term recurrences

Mathematics Subject Classification ID

Iterative numerical methods for linear systems (65F10)

Related Items (6)

A quasi-minimal residual variant of the BiCORSTAB method for nonsymmetric linear systems ⋮ Fast iterative solution of stabilized Navier--Stokes systems ⋮ Variations of Zhang's Lanczos-type product method ⋮ Hybrid Bi-CG methods with a Bi-CG formulation closer to the IDR approach ⋮ Towards backward perturbation bounds for approximate dual Krylov subspaces ⋮ A note on convergence of quasi-minimal residual smoothing

Uses Software

• CGS
• na1

Cites Work

• A breakdown-free Lanczos type algorithm for solving linear systems
• QMR: A quasi-minimal residual method for non-Hermitian linear systems
• Avoiding breakdown and near-breakdown in Lanczos type algorithms
• Avoiding breakdown in variants of the BI-CGSTAB algorithm
• 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 Completed Theory of the Unsymmetric Lanczos Process and Related Algorithms, Part I
• Variants of BICGSTAB for Matrices with Complex Spectrum
• A Completed Theory of the Unsymmetric Lanczos Process and Related Algorithms. Part II
• A Family of Quasi-Minimal Residual Methods for Nonsymmetric Linear Systems
• Residual Smoothing Techniques for Iterative Methods
• A Quasi-Minimal Residual Variant of the Bi-CGSTAB Algorithm for Nonsymmetric Systems
• A Transpose-Free Quasi-Minimal Residual Algorithm for Non-Hermitian Linear Systems

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