Second-order directional derivatives of all eigenvalues of a symmetric matrix
โ Scribed by Mounir Torki
- Publisher
- Elsevier Science
- Year
- 2001
- Tongue
- English
- Weight
- 138 KB
- Volume
- 46
- Category
- Article
- ISSN
- 0362-546X
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๐ SIMILAR VOLUMES
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 direct
Almtraet--Lower and upper bounds on the absolute values of the eigenvalues of an n x n real symmetric matrix A are given by (trace A ,,)t/m for both negative and positive even m. (The bounds are within a factor of 2 from the eigenvalues already for m > log 2 n.) We present algorithms for computing t