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论文类型： 期刊论文

发表时间： 2011-05-15

发表刊物： JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

收录刊物： Scopus、SCIE、EI

卷号： 235

期号： 14

页面范围： 4095-4106

ISSN号： 0377-0427

关键字： Block method; Multiple right-hand sides; Induced dimension reduction IDR(s); Block IDR(s)

摘要： 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 in is the number of right-hand sides. Numerical experiments are presented to show the effectiveness of our proposed method. (C) 2011 Elsevier B.V. All rights reserved.