In this work, a scheme to obtain the SVD from the canonical eigenvalue problems described in Section 1.2 is presented. Methods to approximate both eigenvalues and eigenvectors using the theory of modified moments in conjunction with the Chebyshev semi-iterative method are described. Deflation issues and implicit error approximation methods are addressed to present a complete algorithm. The performance of an ANSI-C implementation of this scheme on a network of UNIX workstations using PVM [9] is presented. The portability of this implementation is demonstrated through results on a 256 processor Cray T3D massively-parallel computer.

The theory of modified moments is discussed in Section 2, followed by a detailed description of the CSI-MSVD algorithm and associated problems in approximating eigenvectors in Section 3. The methodology, test problems, and computational environments used to evaluate the performance of the CSI-MSVD algorithm are described in Section 4. Performance results obtained on two different computing environments (network of workstations and massively-parallel computer system) are presented in Section 5 followed by conclusions and a brief discussion of future work in Section 6.

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

Sun May 19 11:34:27 EDT 1996