Twice differentiable spectral functions

被引：69

作者：

Lewis, AS ^{[1
]}

Sendov, HS ^{[1
]}

机构：

[1] Univ Waterloo, Dept Combinator & Optimizat, Waterloo, ON N2L 3G1, Canada

来源：

SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS | 2001年 / 23卷 / 02期

关键词：

spectral function; twice differentiable; eigenvalue optimization; semidefinite program; symmetric function; perturbation theory;

D O I：

10.1137/S089547980036838X

中图分类号：

O29 [应用数学];

学科分类号：

070104 [应用数学];

摘要：

A function F on the space of n x n real symmetric matrices is called spectral if it depends only on the eigenvalues of its argument. Spectral functions are just symmetric functions of the eigenvalues. We show that a spectral function is twice (continuously) differentiable at a matrix if and only if the corresponding symmetric function is twice (continuously) differentiable at the vector of eigenvalues. We give a concise and usable formula for the Hessian.

引用

页码：368 / 386

页数：19

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