A two-dimensional minimum residual technique foraccelerating two-step iterative solvers۱

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

کلیدواژه ها:

Iterative methods ، minimum residual technique ، convergence ، normalequations ، ill-posed problems