GBi-CGSTAB(\(s,L\)): IDR(\(s\)) with higher-order stabilization polynomials

DOI10.1016/j.cam.2010.07.003zbMath1200.65025OpenAlexW2049617798MaRDI QIDQ708298

Masaaki Tanio, Masaaki Sugihara

Publication date: 11 October 2010

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.2010.07.003

zbMATH Keywords

algorithmnumerical examplesKrylov subspace methodsiterative methods for linear systemsIDR(\(s\))bi-CGSTAB(\(L\))

Mathematics Subject Classification ID

Iterative numerical methods for linear systems (65F10)

Related Items

A quasi-minimal residual variant of IDRstab using the residual smoothing technique ⋮ Iterative processes in the Krylov-Sonneveld subspaces ⋮ IDR: a new generation of Krylov subspace methods? ⋮ IDR(\(s\)) for solving shifted nonsymmetric linear systems ⋮ A variant of the IDR\((s)\) method with the quasi-minimal residual strategy ⋮ An Efficient Variant of the GMRES(m) Method Based on the Error Equations ⋮ A variant of IDRstab with reliable update strategies for solving sparse linear systems ⋮ ML(\(n\))BiCGStabt: a ML(\(n\))BiCGStab variant with \(\mathbf A\)-transpose ⋮ A block IDR\((s)\) method for nonsymmetric linear systems with multiple right-hand sides ⋮ Improvement of preconditioned bi-Lanczos-type algorithms with residual norm minimization for the stable solution of systems of linear equations

Uses Software

• SparseMatrix
• GpBiCg
• CGS

Cites Work

• Unnamed Item
• An iterative method for the Helmholtz equation
• Bi-CGSTAB as an induced dimension reduction method
• BiCGstab(\(l\)) for linear equations involving unsymmetric matrices with complex spectrum
• The university of Florida sparse matrix collection
• 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
• GPBi-CG: Generalized Product-type Methods Based on Bi-CG for Solving Nonsymmetric Linear Systems
• A Lanczos-type method for multiple starting vectors
• Iterative Krylov Methods for Large Linear Systems