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Abstract
Based on the folding method of Evans and Hatzopoulos [5] (see also [1]), in [2] we had described a bi-directional Gaussian elimination algorithm for linear systems Ax= dwith a full general coefficient matrix . Extending these ideas in the present paper we present a parallel Gaussian elimination method suitable for a multiprocessor machine. By partitioning the coefficient matrix
into r
2blocks each of size n × n (N = rn), we introduce a series of transformations L
(k) which at stage
of the process simultaneously eliminate the kth column in each off-diagonal block
and all the elements below the main diagonal in column kof each diagonal block
. The thus transformed system uncouples into rsubsystems each of size n × n with an upper triangular coefficient matrix. The present method has an arithmetical operations count of
which is consistent with the count of
for the standard Gaussian method; thus, the present method could posibly perform with efficiency 2/(3 - 1/r) if implemented on an r-processor machiner≥2.