COMPUTATION OF THE GENERALIZED SINGULAR VALUE DECOMPOSITION USING MESH-CONNECTED PROCESSORS

R. P. BRENT, F. T. LUK, AND CHARLES VAN LOAN

Abstract

This paper concerns the systolic array computation of the generalized singular value decomposition. Numerical algorithms for both one-dimensional and two-dimensional systolic architectures are discussed.

Comments

Only the Abstract is given here. The full paper appeared as [3]. For related work, see [1, 2, 4].

References

1. R. P. Brent, H. T. Kung and F. T. Luk, “Some linear-time algorithms for systolic arrays” (invited paper), in Information Processing 83 (edited by R. E. A. Mason), North-Holland, Amsterdam, 1983, 865–876. rpb079.

2. R. P. Brent, F. T. Luk and C. F. Van Loan, “Computation of the singular value decomposition using mesh-connected processors”, J. of VLSI and Computer Systems 1, 3 (1983–1985), 242–270. MR 86m:65033. rpb080.

3. R. P. Brent, F. T. Luk and C. F. Van Loan, “Computation of the generalized singular value decomposition using mesh-connected processors”, Proceedings SPIE, Volume 431, Real Time Signal Processing VI (edited by Keith Bromley), SPIE, Bellingham, Washington, 1983, 66–71. Also appeared as Report TR 83-563, DCS, Cornell University, July 1983; and as Report CMA-R31-83, CMA, ANU, August 1983, 12 pp. rpb083.

4. R. P. Brent and F. T. Luk, “The solution of singular-value and symmetric eigenvalue problems on multiprocessor arrays”, SIAM J. Scientific and Statistical Computing 6 (1985), 69–84. MR 86i:65089. rpb084.

(Brent) Centre for Mathematical Analysis, Australian National University, Canberra

(Luk, Van Loan) Department of Computer Science, Cornell University, Ithaca, NY 14853

1991 Mathematics Subject Classification. Primary 65Y10; Secondary 47B35, 65F15, 65H17, 65Y05, 68Q22, 68Q25, 68Q35.

Key words and phrases. Systolic arrays, singular-value decomposition, SVD, generalized singular-value decomposition, GSVD, cyclic Jacobi method, real-time computation, VLSI.

The work of the second author was supported in part by the Nationall Science Foundation under grant MCS-8213718, and in part by the Centre for Mathematical Analysis, Australian National University.

Copyright \begin{matrix}c \\ ◯ \end{matrix} 1983, SPIE. Comments \begin{matrix}c \\ ◯ \end{matrix} 1993, R. P. Brent. rpb083a typeset using AMS-L^{A}TEX