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On the direct parallel solution of systems of linear equations: New algorithms and systolic structures

Sridhar, MK and Srinath, R and Parthasarathy, K (1987) On the direct parallel solution of systems of linear equations: New algorithms and systolic structures. In: Information Sciences, 43 (1-2). pp. 25-53.

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Abstract

The paper presents two new algorithms for the direct parallel solution of systems of linear equations. The algorithms employ a novel recursive doubling technique to obtain solutions to an nth-order system in n steps with no more than 2n(n −1) processors. Comparing their performance with the Gaussian elimination algorithm (GE), we show that they are almost 100% faster than the latter. This speedup is achieved by dispensing with all the computation involved in the back-substitution phase of GE. It is also shown that the new algorithms exhibit error characteristics which are superior to GE. An n(n + 1) systolic array structure is proposed for the implementation of the new algorithms. We show that complete solutions can be obtained, through these single-phase solution methods, in 5n−log2n−4 computational steps, without the need for intermediate I/O operations.

Item Type: Journal Article
Additional Information: Copyright of this article belongs to Elsevier Science.
Department/Centre: Division of Electrical Sciences > Electrical Engineering
Date Deposited: 12 Jan 2010 09:30
Last Modified: 12 Jan 2010 09:30
URI: http://eprints.iisc.ernet.in/id/eprint/20464

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