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
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
收藏
页码:72 / 84
页数:13
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