Asymptotic quadratic convergence of the serial block-Jacobi EVD algorithm for Hermitian matrices

被引：8

作者：

Oksa, Gabriel ^{[1
]}

Yamamoto, Yusaku ^{[2
]}

Vajtersic, Marian ^{[1
,3
]}

机构：

[1] Slovak Acad Sci, Inst Math, Bratislava, Slovakia

[2] Univ Electrocommun, Dept Commun Engn & Informat, Tokyo, Japan

[3] Univ Salzburg, Dept Comp Sci, Salzburg, Austria

来源：

NUMERISCHE MATHEMATIK | 2017年 / 136卷 / 04期

基金：

日本科学技术振兴机构;

关键词：

SVD ALGORITHM; ACCURATE;

D O I：

10.1007/s00211-016-0863-5

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We provide the proof of the asymptotic quadratic convergence of the classical serial block-Jacobi EVD algorithm for Hermitian matrices with well-separated eigenvalues (including the multiple ones) as well as clusters of eigenvalues. At each iteration step, two off-diagonal blocks with the largest Frobenius norm are eliminated which is an extension of the original Jacobi approach to the block case. Numerical experiments illustrate and confirm the developed theory.

引用

页码：1071 / 1095

页数：25

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[3]

[Anonymous], 1987, SYMMETRIC EIGENVALUE

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