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.

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Abstract

Parallel Jacobi-like algorithms are presented for computing a singular-value decomposition of an m × n matrix (> 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(n2) 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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