The use of Lanczo's method to solve the large generalized symmetric Eigenvalue problem in parallel

摘要

The generalized eigenvalue problem, K chi = lambda M sub chi, is of significant practical importance, especially in structural engineering where it arises as the vibration and buckling problems. New software, LANZ, based on Lanczo's method was developed for solving these problems and runs on SUN 3, SUN 4, Convex C-220, Cray 2, and Cray Y-MP systems. Preliminary results of using the Force to obtain a multiprocessor implementation of LANZ on MIMD parallel/vector systems are reported. A parallel execution time model of LANZ is defined and used to predict the performance of LANZ as well as examine hypothetical modifications to LANZ. The results of using dynamic shifting to improve parallelism are presented. Finally, the results of assigning a group of processors to separate shifts and finding all the desired eigenvalues using LANZ in parallel are reported.