New techniques for the solution of linear systems by iterative methods

AbstractA new iterative method for the solution of linear systems, based upon a new splitting of the coefficient matrix A, is presented.The method is obtained by considering splittings of the type A = (A − M) + M, where M−1 is a symmetric tridiagonal matrix, and by minimizing the Frobenius norm of the iteration matrix so derived.Numerical examples are provided, showing that our algorithm improves the rate of convergence of Jacobi method, without increasing the order of magnitude of the computational efforts required