A class of optimized row projection methods for solving large non-symmetric linear systems

Abstract

We present in this paper optimal and accelerated row projection algorithms arising from new results that allow us to define the iterate xfc+1 as the projection of xk onto a hyperplane which minimizes its distance to the solution x*. These algorithms also use a novel partition strategy into blocks based on sequential estimations of their condition numbers. Numerical results are given showing the new algorithms are more robust than Krylov subspace based methods, although the latter are generally faster when they converge.