On the condition of the zeros of characteristic polynomials

被引：4

作者：

Buergisser, Peter ^{[1
]}

Cucker, Felipe ^{[2
]}

Cardozo, Elisa Rocha ^{[3
]}

机构：

[1] Tech Univ Berlin, Inst Math, Berlin, Germany

[2] City Univ Hong Kong, Dept Math, Hong Kong, Hong Kong, Peoples R China

[3] Univ Republica, Ctr Matemat, Montevideo, Uruguay

来源：

JOURNAL OF COMPLEXITY | 2017年 / 42卷

关键词：

Eigenvalues; Characteristic polynomial; Condition; Random matrices; MATRICES;

D O I：

10.1016/j.jco.2017.03.004

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

We prove that the expectation of the logarithm of the condition number of each of the zeros of the characteristic polynomial of a complex standard Gaussian matrix is Omega (n) (the real and imaginary parts of the entries of a Gaussian matrix are independent standard Gaussian random variables). This may provide a theoretical explanation for the common practice in numerical linear algebra that advises against computing eigenvalues via root-finding for characteristic polynomials. (C) 2017 Elsevier Inc. All rights reserved.

引用

页码：72 / 84

页数：13