RESIDUAL ELIMINATION ALGORITHM FOR SOLVING LINEAR-EQUATIONS AND APPLICATION FOR SPARSE SYSTEMS

A new direct algorithm for solving linear system of equations will be presented. Short theoretical background and analysis of the proposed m ethod will be given. We formulate an optimized version of the proposed algorithm, which also works for sparse matrices. The complexity of th e suggested algorithm for full matrix systems is n(3)/3+O(n(2)) where n is the dimension of the problem. The numerical experiments show that some versions of the residual elimination algorithm can be competitiv e with the Gaussian elimination both in complexity and precision. More over the sparse linear solver based on this algorithm has some advanta ges in parallel environment.