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A Hessenberg reduction algorithm for rank structured matrices

为等级的一个 HESSENBERG 减小算法组织了矩阵

作     者:Delvaux, Steven Van Barel, Marc 

作者机构:Katholieke Univ Leuven Dept Comp Sci B-3001 Heverlee Belgium 

出 版 物:《SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS》 (工业与应用数学会矩阵分析和应用杂志)

年 卷 期:2007年第29卷第3期

页      面:895-926页

核心收录:

学科分类:07[理学] 070104[理学-应用数学] 0701[理学-数学] 

主  题:rank structured matrix (zero-creating) Givens-weight representation Hessenberg reduction eigenvalue computation singular value computation structure inheritance 

摘      要:In this paper, we show how to perform the Hessenberg reduction of a rank structured matrix under unitary similarity operations in an efficient way, using the Givens-weight representation. This reduction can be used as a first step for eigenvalue computation. We also show how the algorithm can be modified to compute the bidiagonal reduction of a rank structured matrix, this latter method being a preprocessing step for computing the singular values of the matrix. For the main cases of interest, the algorithms we describe in this paper are of complexity O((ar + bs) n(2)), where n is the matrix size, r is some measure for the average rank index of the rank structure, s is some measure for the bandwidth of the unstructured matrix part around the main diagonal, and a,b is an element of R are certain weighting parameters. Numerical experiments demonstrate the stability of this approach.

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