A new Gaussian elimination-based algorithm for parallel solution of linear equations

A variant of Gaussian elimination (GE) method called the successive Gaussian elimination (SGE) algorithm, for the parallel solution of linear equations, is presented. Unlike the conventional GE algorithm, the SGE algorithm does not have a separate back-substitution phase-which requires O(N) steps using O(N) processors or O(log₂ ²N) steps using O(N³) processors-for solving a system of N linear algebraic equations. The SGE algorithm replaces the back-substitution phase by only one step-division-and possesses numerical stability through partial pivoting. Finally, an efficient scheduling scheme for assigning the computational tasks in the SGE algorithm on to the processors in a multiprocessor system is given