A two-dimensional minimum residual technique for accelerating two-step iterative solvers

In this talk, we present a technique to speed up the convergence of a class of two-step iterative methods for solving linear systems of equations. To implement the acceleration technique, the residual norm associated with computed approximations for each sub-iterate is minimized over a certain two-dimensional subspace. Convergence properties of the resulting method will be discussed in detail. It will be further shown that the approach can be developed to solve (regularized) normal equations arising from the discretization of ill-posed problems. Numerical experiments will be disclosed to illustrate the performance of exact and inexact variants of the method for some test problems.