The Lanczos algorithm for the generalized symmetric eigenproblem on shared-memory architectures

The generalized eigenvalue problem, Kx = {lambda}Mx, is of significant practical importance, for example, in structural engineering where it arises as the vibration and buckling problems. The paper describes the implementation of a solver based on the Lanczos algorithm, LANZ, on two shared-memory architectures, the CRAY Y-MP and Encore Multimax. Issues arising from implementing linear algebra operations on a multivector processor are examined. Portability between a multivector processor and a simple multiprocessor is discussed. A model is developed and used to predict the performance of LANZ on shared-memory architectures. Performance results from some practical problems are given and analyzed. 20 refs., 5 figs