A Sherman–Morrison approach to the solution of linear systems

We propose a new direct method to solve linear systems. This method is based on the Sherman–Morrison formula and uses a finite iterative formula. To compare our method with the Restarted Generalized Minimum Residual Method and the Gaussian Elimination Method with Partial Pivoting, we use two classes of test problems: linear systems having Pascal, Cauchy, and Vandermonde matrices as coefficient matrices, and randomly generated linear systems.