Second-order directional derivatives of spectral functions

S. J. Li; K. L. Teo; Xiaoqi Yang

doi:10.1016/j.camwa.2004.11.021

Second-order directional derivatives of spectral functions

S. J. Li, K. L. Teo, Xiaoqi Yang

Research output: Journal article publication › Journal article › Academic research › peer-review

Abstract

A spectral function of a symmetric matrix X is a function which depends only on the eigenvalues of X, λ1(X) < λ2(X) << λn(X), and may be written as f (λ1(X), λ2(X), , λn(X)) for some symmetric function f. In this paper, we assume that f is a C1,1function and discuss second-order directional derivatives of such a spectral function. We obtain an explicit expression of second-order directional derivative for the spectral function.

Original language	English
Pages (from-to)	947-955
Number of pages	9
Journal	Computers and Mathematics with Applications
Volume	50
Issue number	5-6
DOIs	https://doi.org/10.1016/j.camwa.2004.11.021
Publication status	Published - 1 Sept 2005

Keywords

Nonsmooth analysis
Second-order directional derivative
Spectral function

ASJC Scopus subject areas

Modelling and Simulation
Computational Theory and Mathematics
Computational Mathematics

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10.1016/j.camwa.2004.11.021

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N2 - A spectral function of a symmetric matrix X is a function which depends only on the eigenvalues of X, λ1(X) < λ2(X) << λn(X), and may be written as f (λ1(X), λ2(X), , λn(X)) for some symmetric function f. In this paper, we assume that f is a C1,1function and discuss second-order directional derivatives of such a spectral function. We obtain an explicit expression of second-order directional derivative for the spectral function.

AB - A spectral function of a symmetric matrix X is a function which depends only on the eigenvalues of X, λ1(X) < λ2(X) << λn(X), and may be written as f (λ1(X), λ2(X), , λn(X)) for some symmetric function f. In this paper, we assume that f is a C1,1function and discuss second-order directional derivatives of such a spectral function. We obtain an explicit expression of second-order directional derivative for the spectral function.

KW - Nonsmooth analysis

KW - Second-order directional derivative

KW - Spectral function

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U2 - 10.1016/j.camwa.2004.11.021

DO - 10.1016/j.camwa.2004.11.021

M3 - Journal article

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JO - Computers and Mathematics with Applications

JF - Computers and Mathematics with Applications

IS - 5-6

ER -

Second-order directional derivatives of spectral functions

Abstract

Keywords

ASJC Scopus subject areas

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