Exploiting BiCGstab(?) strategies to induce dimension reduction

Journal article (2010)
Department
Delft Institute of Applied Mathematics (EEMCS) (TU Delft)
Copyright: Society for Industrial and Applied Mathematics
DOI: https://doi.org/doi:10.1137/090752341
Krylov subspace methods Bi-CGSTAB Bi-CG Iterative linear solvers Induced dimension reduction
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Published Date

31-08-2010

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Source:

SIAM Journal on Scientific Computing, 32 (5), 2010

ISSN:

1064-8275

Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Delft Institute of Applied Mathematics

Abstract

IDR(s) [P. Sonneveld and M. B. van Gijzen, SIAM J. Sci. Comput., 31 (2008), pp. 1035–1062] and BiCGstab(?) [G. L. G. Sleijpen and D. R. Fokkema, Electron. Trans. Numer. Anal., 1 (1993), pp. 11–32] are two of the most efficient short-recurrence iterative methods for solving large nonsymmetric linear systems of equations. Which of the two is best depends on the specific problem class. In this paper we describe IDRstab, a new method that combines the strengths of IDR(s) and BiCGstab(?). To derive IDRstab we extend the results that we reported on in [G. L. G. Sleijpen, P. Sonneveld, and M. B. van Gijzen, Appl. Numer. Math., (2009), DOI: 10.1016/j.apnum.2009.07.001], where we considered Bi-CGSTAB as an induced dimension reduction (IDR) method. We will analyze the relation between hybrid Bi-CG methods and IDR and introduce the new concept of the Sonneveld subspace as a common framework. Through numerical experiments we will show that IDRstab can outperform both IDR(s) and BiCGstab(?).