Second-Order Directional Derivatives of Spectral Functions
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 der...
| Main Authors: | , , |
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| Format: | Journal Article |
| Published: |
Pergamon
2005
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| Online Access: | http://hdl.handle.net/20.500.11937/26829 |
| _version_ | 1848752096738803712 |
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| author | Li, S. Teo, Kok Lay Yang, X. |
| author_facet | Li, S. Teo, Kok Lay Yang, X. |
| author_sort | Li, S. |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | 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. |
| first_indexed | 2025-11-14T08:03:11Z |
| format | Journal Article |
| id | curtin-20.500.11937-26829 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T08:03:11Z |
| publishDate | 2005 |
| publisher | Pergamon |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-268292017-09-13T15:30:00Z Second-Order Directional Derivatives of Spectral Functions Li, S. Teo, Kok Lay Yang, X. 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. 2005 Journal Article http://hdl.handle.net/20.500.11937/26829 10.1016/j.camwa.2004.11.021 Pergamon unknown |
| spellingShingle | Li, S. Teo, Kok Lay Yang, X. Second-Order Directional Derivatives of Spectral Functions |
| title | Second-Order Directional Derivatives of Spectral Functions |
| title_full | Second-Order Directional Derivatives of Spectral Functions |
| title_fullStr | Second-Order Directional Derivatives of Spectral Functions |
| title_full_unstemmed | Second-Order Directional Derivatives of Spectral Functions |
| title_short | Second-Order Directional Derivatives of Spectral Functions |
| title_sort | second-order directional derivatives of spectral functions |
| url | http://hdl.handle.net/20.500.11937/26829 |