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

摘要

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. Geradin, 1984), physics (e.g. Rappaz, 1979), chemistry (e.g. Davidson, 1983), econ- omy (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 numeri- cal difficulties in relation to its sensivity to roundoff errors that may lead to numerical unstabilities, particularly if the eigenvalues are not well separated.