## Computation of the SVD using mesh-connected processors

80. 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.
Abstract:
dvi (3K),
pdf (80K),
ps (28K).

Paper:
pdf (2385K).

## Abstract

A cyclic Jacobi method for computing the singular value decomposition of
an *m* × *n*
matrix (*m *__>__ n)
using systolic arrays is proposed.
The algorithm requires O(*n*^{2})
processors and O(*m + n* log *n*)
units of time.

## Comments

The systolic array proposed here is similar to one proposed
by Brent and Luk [84] for the symmetric
eigenvalue problem, but to handle a rectangular SVD problem requires
a preprocessing step in which a QR factorization is computed.
A closely related paper is [87].
For an extension to the generalized SVD, see [83].

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