A block IDR(s) method for nonsymmetric linear systems with multiple right-hand sides

Authors:
L. Du;T. Sogabe;B. Yu;Y. Yamamoto;S. -L. Zhang
Affiliations:
Department of Computational Science and Engineering, Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-8603, Japan;Graduate School of Information Science and Technology, Aichi Prefectural University, Nagakute-cho, Aichi-gun, Aichi, 480-1198, Japan;School of Mathematical Sciences, Dalian University of Technology, Dalian, Liaoning, 116024, PR China;Department of Computer Science and Systems Engineering, Kobe University, Rokkodai-cho, Nada-ku, Kobe, 657-8501, Japan;Department of Computational Science and Engineering, Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-8603, Japan
Venue:
Journal of Computational and Applied Mathematics
Year:
2011

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Abstract

The IDR(s) based on the induced dimension reduction (IDR) theorem, is a new class of efficient algorithms for large nonsymmetric linear systems. IDR(1) is mathematically equivalent to BiCGStab at the even IDR(1) residuals, and IDR(s) with s1 is competitive with most Bi-CG based methods. For these reasons, we extend the IDR(s) to solve large nonsymmetric linear systems with multiple right-hand sides. In this paper, a variant of the IDR theorem is given at first, then the block IDR(s), an extension of IDR(s) based on the variant IDR(s) theorem, is proposed. By analysis, the upper bound on the number of matrix-vector products of block IDR(s) is the same as that of the IDR(s) for a single right-hand side in generic case, i.e., the total number of matrix-vector products of IDR(s) may be m times that of of block IDR(s), where m is the number of right-hand sides. Numerical experiments are presented to show the effectiveness of our proposed method.