Eigenvalue Solvers For Large Problems

. This paper addresses the question of the form library routine eigenvalue solvers for large--scale problems should take. Because such solvers are capable of producing an embarassing amount of information (for example, all eigenvectors of an n \Theta n matrix emphasis is put on providing users with the capability to be selective in their computing options in addition to the usual emphasis on efficient algorithms for parallel and vector computation. Examples considered include: (i) symmetric tridiagonal eigenvalue solvers which produce user specified ordered subsets of the eigenvalues in a two--phase algorithm which uses multisectioning in order to isolate the eigenvalues followed by a third order convergent technique to refine eigenvalue estimates and compute eigenvectors; (ii) solvers for general problems which find a prescribed number of eigenvalues and eigenvectors starting from a user supplied initial point. Here relevant points include taking advantage of sparse structure, the eas..