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.
- Nonsmooth analysis
- Second-order directional derivative
- Spectral function
ASJC Scopus subject areas
- Modelling and Simulation
- Computational Theory and Mathematics
- Computational Mathematics