Second-order directional derivatives of spectral functions

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

Research output: Journal article publicationJournal articleAcademic researchpeer-review


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 languageEnglish
Pages (from-to)947-955
Number of pages9
JournalComputers and Mathematics with Applications
Issue number5-6
Publication statusPublished - 1 Sep 2005


  • 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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