Abstract
ABSTRACT We present two new parallel algorithms for exact (error-free) solution of a system of linear equations on a distributed-memory multiprocessor. The exact solution is obtained using the congruence technique which consists of two steps: First, the system of linear equations is converted to systems of linear congruence equations with respect to several prime moduli, and each of these systems is solved on a separate processor. Then, these solutions are combined using the mixed-radix conversion algorithm to obtain the exact solution. The first step is completely (embarrassingly) parallel with no communication requirements among the processors. We improve our previous work and describe two efficient parallel algorithms for the second step. We present the results of our experiments on an Intel iPSC/860 with 8 processors. A linear system of dimension 128 with integer entries as large as 10577 is solved in about 195 seconds on 8 processors with an efficiency of 99.76%.
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