A new and faster Gaussian elimination based fault tolerant systolic linear system solver

This paper presents a new systolic algorithm for the complete solution of a system of N linear equations in (N-2/2 + O (N)) time steps using 2N processing elements (PEs). It is based on a variant of the Gaussian elimination (GE) algorithm called the successive GE and is faster than any existing GE based algorithm using O(N) PEs. We also suggest two fault tolerant schemes that tolerate up to N PE failures. The first scheme is a time redundancy based approach with no hardware overhead and 100% time overhead. This scheme can tolerate up to N PE failures, The second scheme is based on algorithm based fault tolerance (ABFT) and uses N extra PEs to tolerate up to N - 1 PE failures with very little time overhead. The number of errors that can be detected/corrected in both schemes is more than that in any existing fault tolerant systolic array. (C) 1997 Academic Press.