A note on polar decomposition based Gersgorin-type sets

被引：1

作者：

Smithies, Laura ^{[1
]}

机构：

[1] Kent State Univ, Dept Math Sci, Kent, OH 44242 USA

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2008年 / 429卷 / 10期

关键词：

Polar decomposition; Gersgorin type sets; Normal matrices; Eigenvalue estimates;

D O I：

10.1016/j.laa.2008.04.049

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let B is an element of C-nxn denote a finite-dimensional square complex matrix. In [L. Smithies, R.S. Varga, Singular value decomposition Gersgorin sets, J. Linear Algebra Appl. 417 (2004) 370-380; N. Fontes, J. Kover, L. Smithies, R.S. Varga, Singular value decomposition normally estimated Gersgorin sets, Electron. Trans. Numer. Anal. 26 (2007) 320-329], Professor Varga and I introduced Gersgorin-type sets which were developed from singular value decompositions (SVDs) of B. In this note, our work is extended by introducing the polar SV-Gersgorin set, Gamma(PSV)(B). The set Gamma(PSV)(B) is a union of n closed discs in C, whose centers and radii are defined in terms of the entries of a polar decomposition B = Q vertical bar B vertical bar. The set of eigenvalues of B, sigma (B), is contained in Gamma(PSV)(B). (C) 2008 Elsevier Inc. All rights reserved.

引用

页码：2623 / 2627

页数：5