Adaptive Richardson iteration based on Leja points

An adaptive Richardson iteration method is presented for the solution of large linear systems of equations with a sparse symmetric positive definite matrix. The relaxation parameters for Richardson iteration are chosen to be reciprocal values of Leja points for an interval [a, b] on the positive real axis, and the endpoints a and b are determined adaptively by computing certain modified moments during the iterations. Computed examples show that the adaptive Richardson method can be competitive with the conjugate gradient algorithm.