In this section, the performance of PVM implementations of the CSI-MSVD algorithm (for two-cyclic matrices) is presented along with improvements to and comparisons with Krylov subspace methods (Lanczos and Arnoldi). For most of the test matrices from Section 4.3, the error estimate defined by Equation (31) provided a suitable upper bound on the actual error in singular vectors when as many as 10 of the largest singular triplets were approximated by CSI-MSVD to accuracy (see [22]). The implementation on a network of workstations was based on ANSI C with PVM Version 3.3.7. A brief overview of the parallel implementation is presented in Section 5.3, and the associated performance in terms of scalability is discussed in Section 5.4. Issues such as load balancing are discussed in more in detail in [22]. Finally, the performance of the PVM implementation of the CSI-MSVD algorithm on the Cray T3D is described in Section 5.5.

- 5.1 Comparison with Lanczos Algorithm
- 5.2 Preconditioner for Arnoldi's method
- 5.3 Components of the Parallel Implementation
- 5.4 Scalability
- 5.5 Results of Cray T3D Implementation

Michael W. Berry (berry@cs.utk.edu)

Sun May 19 11:34:27 EDT 1996