Sub-gradient algorithms for computation of extreme eigenvalues of a real symmetric matrix

• Autorzy: Yassine A.
• Języki publikacji: EN

Abstrakty

EN

The computation of eigenvalues of a matrix is still of importance from both theoretical and practical points of view. This is a significant problem for numerous industrial and scientific situations, notably in dynamics of structures (e.g. Gerardin, 1984), physics (e.g. Rappaz, 1979), chemistry (e.g. Davidson, 1983), economy (e.g. Morishima, 1971; Neumann, 1946), mathematics (e.g. Golub, 1989; Chatelin, 1983, 1984, 1988). The study of eigenvalue problems remains a delicate task, which generally presents numerical difficulties in relation to its sensivity to roundoff errors that may lead to numerical unstabilities, particularly if the eigenvalues are not well separated. In this paper, new subgradient-algorithms for computation of extreme eigenvalues of a symmetric real matrix are presented. Those algorithms are based on stability of Lagrangian duality for non-convex optimization and on duality in the difference of convex functions. Some experimental results which prove the robustness and efficiency of our algorithms are provided.

Słowa kluczowe

EN

difference of convex functions; eigenvalue problems; Lagrangian duality; non-convex optimization; sub-gradient algorithms

PL

problem wartości własnej

• Wydawca: Systems Research Institute, Polish Academy of Sciences
• Czasopismo: Control and Cybernetics
• Rocznik: 1998
• Tom: Vol. 27, no 3
• Strony: 387--415
• Opis fizyczny: Bibliogr. 23 poz.,Tab., wykr.,

Twórcy

autor

Yassine A.