A New Algorithm Based on Givens Rotations for Solving Linear Equations on Fault-Tolerant Mesh-Connected Processors
Issue No. 08 - August (1998 vol. 9)
DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/71.706053
<p><b>Abstract</b>—In this paper, we propose a new <it>I/O overhead free</it> Givens rotations based parallel algorithm for solving a system of linear equations. The algorithm uses a new technique called <it>two-sided elimination</it> and requires an <it>N</it>× (<it>N</it> + 1) mesh-connected processor array to solve <it>N</it> linear equations in (5<it>N</it><tmath>$-$</tmath><it>log N</it><tmath>$-$</tmath> 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.</p>
Linear equations, Givens rotations, parallel algorithm, mesh-connected processor array, fault tolerance.
K. Bhuvaneswari, C. Siva Ram Murthy and K. Balasubramanya Murthy, "A New Algorithm Based on Givens Rotations for Solving Linear Equations on Fault-Tolerant Mesh-Connected Processors," in IEEE Transactions on Parallel & Distributed Systems, vol. 9, no. , pp. 825-832, 1998.