The Use of Lanczo's Method to Solve the Large Generalized Symmetric Eigenvalue Problem in Parallel
INSTITUTE FOR COMPUTER APPLICATIONS IN SCIENCE AND ENGINEERING HAMPTON VA
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The generalized eigenvalue problem, KxLamdaMx, is of significant practical importance, especially in structural engineering where it arises as the vibration and buckling problems. New software, LANZ, based on Lanczos method has been developed for solving these problems and uns 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 parallelvector systems are reported here. 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. Keywords Eigenvalues Parallel orientation Mathematical methods Computer software Computer systems.
- Theoretical Mathematics