A parallel ring ordering algorithm
for efficient one-sided Jacobi SVD computations
153. B. B. Zhou and R. P. Brent,
A parallel ring ordering algorithm
for efficient one-sided Jacobi SVD computations,
J. Parallel and Distributed Computing 42 (1997), 1-10.
Paper:
dvi (37K),
pdf (113K),
ps (67K).
Abstract
In this paper we give evidence to show that
in one-sided Jacobi SVD computation the sorting of column norms in each
sweep is very important.
An efficient parallel ring Jacobi ordering for computing
singular value decomposition is described.
This ordering can generate n(n-1)/2 different index pairs
and sort column norms at the same time.
The one-sided Jacobi SVD algorithm using this parallel ordering converges
in about the same number of sweeps as the
sequential cyclic Jacobi algorithm.
The issue of equivalence of orderings for one-sided
Jacobi is also discussed. We show how an ordering which does not sort column
norms into order may still perform efficiently as long as it can generate the
same index pairs at the same step as one which does sorting.
Some experimental results obtained on a Fujitsu AP1000 are presented.
Notes
A closely related (but shorter) paper is [154].
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