Second-Order Directional Derivatives of Spectral Functions

Li, S.; Teo, Kok Lay; Yang, X.

doi:10.1016/j.camwa.2004.11.021

Access Status

Open access via publisher

Authors

Li, S.

Teo, Kok Lay

Yang, X.

Date

2005

Type

Journal Article

Metadata

Show full item record

Citation

Li, S. and Teo, K.L. and Yang, X. 2005. Second-Order Directional Derivatives of Spectral Functions. Computers and Mathematics with Applications. 50 (5-6): pp. 947-955.

Source Title

Computers and Mathematics with Applications

DOI

10.1016/j.camwa.2004.11.021

ISSN

08981221

School

Department of Mathematics and Statistics

URI

http://hdl.handle.net/20.500.11937/26829

Collection

Curtin Research Publications

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 ƒ (λ1 (X), λ2(X), , λn (X)) for some symmetric function ƒ. In this paper, we assume that ƒ is a C1,1 function 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.