A two-dimensional minimum residual technique for accelerating two-step iterative solvers with applications to discrete ill-posed problems

03/22/2023

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by   Fatemeh P. A. Beik, et al.

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This paper deals with speeding 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 proposed method are studied in detail. The approach is further developed to solve (regularized) normal equations arising from the discretization of ill-posed problems. The results of numerical experiments are reported to illustrate the performance of exact and inexact variants of the method for some test problems.