Abstract
Solving large, linear systems is among the most important and most frequently encountered problems in computational mathematics and computer science. This paper presents efficient parallel Jacobi and Gauss-Seidel algorithms, in spite of the apparent inherent sequentiality of the latter, for the iterative solution of large linear systems on hypercube machines. To evaluate their performance, expressions for the speedup factor of the algorithms are derived. The results show that the hypercubes are highly effective in solving large systems of dense linear algebraic equations. Finally, the suitability of the hypercubes for solving sparse linear systems is discussed.
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