An iterative solution method for solving sparse nonsymmetric linear systems

Abstract

An algorithm is presented for the general solution of a set of linear equations Ax= b. The method works exceptionally well for the solution of large sparse systems of linear equations, the co-efficient matrix A of which need not be symmetric but should have workable splits. The method can be applied to problems which arise in convection-diffusion, flow of fluids and oil reservoir modeling. The difference of the upper secondary diagonals (super diagonals) and the lower secondary diagonals (sub diagonals) of the matrix A leads to a decomposition of A into a difference of a symmetric matrix, having the same lower structure as that of A, and a strictly upper triangular matrix. The symmetric matrix is made diagonally dominant and the system is solved iteratively.