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A New Algorithm Based on Givens Rotations for Solving Linear Equations on Fault-Tolerant Mesh-Connected Processors
August 1998 (vol. 9 no. 8)
pp. 825-832

Abstract—In this paper, we propose a new I/O overhead free Givens rotations based parallel algorithm for solving a system of linear equations. The algorithm uses a new technique called two-sided elimination and requires an N× (N + 1) mesh-connected processor array to solve N linear equations in (5N$-$log N$-$ 4) time steps. The array is well suited for VLSI implementation as identical processors with simple and regular interconnection pattern are required. We also describe a fault-tolerant scheme based on an algorithm based fault tolerance (ABFT) approach. This scheme has small hardware and time overhead and can tolerate up to N processor failures.

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Index Terms:
Linear equations, Givens rotations, parallel algorithm, mesh-connected processor array, fault tolerance.
K.n. Balasubramanya Murthy, K. Bhuvaneswari, C. Siva Ram Murthy, "A New Algorithm Based on Givens Rotations for Solving Linear Equations on Fault-Tolerant Mesh-Connected Processors," IEEE Transactions on Parallel and Distributed Systems, vol. 9, no. 8, pp. 825-832, Aug. 1998, doi:10.1109/71.706053
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