GPBiCG(m, l): a hybrid of BiCGSTAB and GPBiCG methods with efficiency and robustness

Authors:
Seiji Fujino
Affiliations:
Kyushu University, Computing and Communications Center, 6-10-1 Hakozaki, Higashi-ku, Fukuoka, 812-8581, Japan
Venue:
Applied Numerical Mathematics - Developments and trends in iterative methods for large systems of equations—in memoriam Rüdiger Weiss
Year:
2002

Citing 5
Cited 1

CGS, a fast Lanczos-type solver for nonsymmetric linear systems

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BI-CGSTAB: a fast and smoothly converging variant of BI-CG for the solution of nonsymmetric linear systems

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Lanczos methods for the solution of nonsymmetric systems of linear equations

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Variants of BICGSTAB for matrices with complex spectrum

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GPBi-CG: Generalized Product-type Methods Based on Bi-CG for Solving Nonsymmetric Linear Systems

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Minimizing synchronizations in sparse iterative solvers for distributed supercomputers

Computers & Mathematics with Applications

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Abstract

In this paper a new iterative method which is a hybrid of the BiCGSTAB and GPBiCG methods is proposed. The present method is an extension of the BiCGSTAB2 method. In the BiCGSTAB2 method which is a hybrid type method, two parameters of the BiCGSTAB method are adopted at even iteration step, and those of the GPBiCG method are used at odd iteration step. In the present GPBiCG(m, l) method, parameters of the BiCGSTAB method are adopted at consecutive m iteration steps, and afterwards those of the GPBiCG method are also utilized in succession at l iteration steps. We will examine the convergence property of the GPBiCG(m, l) method and investigate its effectiveness through numerical experiments.