Computing the minimum eigenvalue of symmetric positive definite Toeplitz matrix by Newton-type methods

被引：9

作者：

Mackens, W ^{[1
]}

Voss, H ^{[1
]}

机构：

[1] Tech Univ Hamburg, Arbeitsbereich Math, D-21073 Hamburg, Germany

来源：

SIAM JOURNAL ON SCIENTIFIC COMPUTING | 2000年 / 21卷 / 04期

关键词：

Toeplitz matrix; eigenvalue problem; Newton's method;

D O I：

10.1137/S1064827598342195

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A method for computing the smallest eigenvalue of a symmetric positive definite Toeplitz matrix by application of Newton's method to the characteristic polynomial has been recently introduced by Mastronardi and Boley [SIAM J. Sci. Comput., 20 (1999), pp. 1921-1927]. Though considerably slower than methods developed by the authors [W. Mackens and H. Voss, SIAM J. Matrix. Anal. Appl., 18 (1997), pp. 521-534], [W. Mackens and H. Voss, Linear Algebra Appl., 275/276 (1998), pp. 401-415], [H. Voss, Linear Algebra Appl., 287 (1999), pp. 359-371] the new approach is conceptually much simpler. In this paper we improve the performance of the new method substantially while keeping its simplicity.

引用

页码：1650 / 1656

页数：7

共 50 条

[1] Computing the minimum eigenvalue of a symmetric positive definite Toeplitz matrix by Newton-type methods
Tech. Univ. Hamburg-Harburg, Arbeitsbereich Mathematik, Schwarzenbergstrasse 95, D-21073 Hamburg, Germany
[J]. Siam J. Sci. Comput, 4 (1650-1656):
[2] A projection method for computing the minimum eigenvalue of a symmetric positive definite Toeplitz matrix
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[J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 1998, 276 : 401 - 415
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[J]. Linear Algebra and Its Applications, 1998, 275-176 : 401 - 415
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