A matrix nearness problem related to iterative methods

被引:7
|
作者
Huhtanen, M [1 ]
机构
[1] Helsinki Univ Technol, Inst Math, FIN-02150 Espoo, Finland
关键词
nearness problem; iterative methods; short term recurrence;
D O I
10.1137/S0036142999363620
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We consider a matrix nearness problem arising from an analysis of the speed of convergence of GMREs for solving a linear system Ax = b with A is an element of C-nxn and b is an element of C-n. More precisely, denoting by F-k the set of matrices of rank k at most, we solve [GRAPHICS] where S subset of C-nxn denotes the set of matrices of the form e(i theta) H - lambdaI with theta is an element of [0, 2 pi), lambda is an element of C, and H belonging to the set of Hermitian matrices. As to iterative methods, the set S is of interest in a larger context. To give an example, having a regular splitting A = S + F-k of A, the system Ax = b can be solved using a (k+3)-term recurrence with inner-outer iterations.
引用
收藏
页码:407 / 422
页数:16
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