A PARALLEL DIVIDE AND CONQUER ALGORITHM FOR NON SYMMETRIC TRIDIAGONAL TOEPLITZ SYSTEMS USING CONJUGATE GRADIENT

Abstract In this paper, we consider the application of the conjugate gradient method specifically to solve non symmetric systems which are large, tridiagonal and Toeplitz. Under the condition that the system is diagonally dominant, one can pre-multiply the system by the transpose of the coefficient matrix and take advantage of the structure of the new coefficient matrix to perturb and factor it. This allows us to divide the task of solution containing pairs of tridiagonal, symmetric and Toeplitz systems and to solve the pairs of systems using a parallel implementaton of congujate gradient. Final corrections, to account for the perturbations, provide a numerical approximation to the solution.