Performance Evaluation of Parallel Gram-Schmidt Re-orthogonalization Methods
In this paper, the performance of the five kinds of parallel reorthogonalization methods by using the Gram-Schmidt (G-S) method is reported. Parallelization of the re-orthogonalization process depends on the implementation of G-S orthogonalization process, i.e. Classical G-S (CG-S) and Modified G-S (MG-S). To relax the parallelization problem, we propose a new hybrid method by using both the CG-S and MG-S. The HITACHI SR8000/MPP of 128 PEs, which is a distributed memory super-computer, is used in this performance evaluation.
Unable to display preview. Download preview PDF.
- S. Balay, W. Gropp, L. C. McInnes, and B. Smith. Petsc 2.0 users manual, 1995. ANL-95/11-Revision 2.0.24, http://www-fp.mcs.anl.gov/petsc/. 309
- J.W. Demmel. Applied Numerical Linear Algebra. SIAM, 1997. 302Google Scholar
- J. J. Dongarra, I. S. Du., D.C. Sorensen, and H.A. van der Vorst. Numerical Linear Algebra for High-Performance Computers. SIAM, 1998. 302Google Scholar
- T. Katagiri. A study on parallel implementation of large scale eigenproblem solver for distributed memory architecture parallel machines. Master’s Degree Thesis, the Department of Information Science, the University of Tokyo, 1998. 302Google Scholar
- T. Katagiri. A study on large scale eigensolvers for distributed memory parallel machines. Ph.D Thesis, the Department of Information Science, the University of Tokyo, 2000. 302, 303, 304Google Scholar
- B.N. Parlett. The Symmetric Eigenvalue Problem. SIAM, 1997. 302, 308, 309Google Scholar
- G.W. Stewart. Matrix Algorithms Volume II:Eigensystems. SIAM, 2001. 302Google Scholar
- D. Vanderstraeten. A parallel block gram-schmidt algorithm with controlled loss of orthogonality. Proceedings of the Ninth SIAM Conference on Parallel Processing for Scientific Computing, 1999. 302Google Scholar
- Y. Yamamoto, M. Igai, and K. Naono. A new algorithm for accurate computation of eigenvectors on shared-memory parallel processors. Proceedings of Joint Symposium on Parallel Processing (JSPP)’2000, pages 19–26, 2000. in Japanese. 302Google Scholar