A multiprocessor scheme for the singular value decomposition
We present a multiprocessor scheme for determining the singular value decomposition of rectangular matrices in which the number of rows is substantially large (or smaller) than the number of columns. In this scheme, we perform an initial QR factorization on the tall matrix (either A or A/sup T/) using a multiprocessor block Householder algorithm. We then use a parallel one-sided Jacobi scheme to orthogonalize the columns of the upper triangular matrix R to yield the factorization RV = U..sigma.., from which the desired singular value decomposition is obtained. Preliminary experiments on an Alliant FX/8 computer system with 8 processors indicate speedups near 5 for our scheme over an optimized implementation of the Linpack/Eispack routines which perform the classical bi-diagonalization technique. Our scheme performs exceptionally well for rank deficient matrices as well as for those rectangular matrices having clustered or multiple singular values, and may be well suited for applications such as real-time signal processing. We present performance results on the Alliant FX/8 and Cray X-MP/48 computer systems with particular emphasis on speedups obtained for our scheme over classical SVD algorithms.
- Research Organization:
- Illinois Univ., Urbana (USA). Center for Supercomputing Research and Development
- DOE Contract Number:
- FG02-85ER25001
- OSTI ID:
- 5576354
- Report Number(s):
- DOE/ER/25001-52; CONF-871251-2; ON: DE88003591
- Resource Relation:
- Conference: 3. SIAM conference on parallel processing for scientific computing, Los Angeles, CA, USA, 1 Dec 1987; Other Information: Portions of this document are illegible in microfiche products
- Country of Publication:
- United States
- Language:
- English
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