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Second-order directional derivatives of spectral functions

โœ Scribed by S.J. Li; K.L. Teo; X.Q. Yang

Publisher
Elsevier Science
Year
2005
Tongue
English
Weight
370 KB
Volume
50
Category
Article
ISSN
0898-1221

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โœฆ Synopsis

A spectral function of a symmetric matrix X is a function which depends only on the eigenvalues of X, A1 (X) ~ A2 (X) ~.-. > An (X), and may be written as .f(A1 (X), A2(X) ..... An (X)) for some symmetric function /. In this paper, we assume that / is a C 1,1 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. ~) 2005 Elsevier Ltd. All rights reserved.

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