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On reduction schemes and the symmetry of a matrix

✍ Scribed by Ren, Gexue ;Cheng, Jiangang ;Jinwu, Xiang ;Lu, Qiuhai

Publisher: John Wiley and Sons
Year: 1999
Tongue: English
Weight: 88 KB
Volume: 15
Category: Article
ISSN: 1069-8299
DOI: 10.1002/(sici)1099-0887(199909)15:9<679::aid-cnm282>3.0.co;2-s

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✦ Synopsis

In this paper, Lanczos and Arnoldi reduction methods as the special cases of the generalized Hessenberg method are brie¯y reviewed. Attention is paid to the eect of symmetry of matrices on the behaviour of the reduction schemes, such as serious numerical breakdown. Based on the summation decomposition of matrices, two structures of the upper Hessenberg form of a general unsymmetric matrix and their relationship are revealed, in terms of which, Arnoldi reduction schemes for unsymmetric matrices can be reformulated in two respective forms. The relationship between the reformulated reduction scheme and the current Lanczos schemes for skew and symmetric matrices are also discussed.

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