## The solution of singular-value and symmetric
eigenvalue problems on multiprocessor arrays

84. 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.
A preliminary version appeared in
* Proceedings of a Workshop on Mathematical Programming
and Numerical Analysis*
(edited by S. Gustavson and R.S. Womersley),
CMA, ANU, 1984, 38-64.
MR 86k:65129.

Abstract:
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Paper: pdf (1504K).

## Abstract

Parallel Jacobi-like algorithms are presented for computing a
singular-value decomposition of an
*m* × *n* matrix
(*m *__>__ n) and an eigenvalue decomposition of an
*n* × *n* symmetric matrix.
A linear array of O(*n*)
processors is proposed for the singular-value problem; the associated
algorithm requires time O(*mnS*), where *S* is
the number of sweeps (typically *S* __<__ 10).
It is conjectured that *S* = O(log *n*).
A square array of O(*n*^{2}) processors with
nearest-neighbor communication is proposed for the eigenvalue problem;
the associated algorithm requires time O(*nS*).
## Comments

This paper incorporates revisions of the two Reports
[75,
76].
For related work, see
[79,
80,
83,
86,
87,
107,
137].
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