Article ID Journal Published Year Pages File Type
4640007 Journal of Computational and Applied Mathematics 2011 12 Pages PDF
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 s>1 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.
Related Topics
Physical Sciences and Engineering Mathematics Applied Mathematics
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