THE STRUCTURED DISTANCE TO NEARLY NORMAL MATRICES

被引：0

作者：

Smithies, Laura ^{[1
]}

机构：

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

来源：

ELECTRONIC TRANSACTIONS ON NUMERICAL ANALYSIS | 2009年 / 36卷

关键词：

nearness to normality; tridiagonal matrix; Krein spaces; eigenvalue estimation; Gersgorin type sets;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this note we examine the algebraic variety I-Lambda of complex tridiagonal n x n matrices T, such that T*T - TT* = Lambda, where Lambda is a fixed real diagonal matrix. If Lambda = 0 then I-Lambda is N-T, the set of tridiagonal normal matrices. For Lambda not equal 0, we identify the structure of the matrices in I-Lambda and analyze the suitability for eigenvalue estimation using normal matrices for elements of I-Lambda. We also compute the Frobenius norm of elements of I-Lambda, describe the algebraic subvariety M-Lambda consisting of elements of I-Lambda with minimal Frobenius norm, and calculate the distance from a given complex tridiagonal matrix to I-Lambda.

引用

页码：99 / 112

页数：14

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