A convergence theorem on an extrapolated iterative method and its applications (Q1294476)

The elementary, but very useful, concept of the extrapolation or relaxation is generally used to accelerate iterative methods for solving linear systems, but its convergence conditions were not studied thoroughly. In this note, a new result on the convergence of an extrapolated iterative method is derived. Furthermore, necessary and sufficient conditions on its convergence are given. As its applications, we discuss the convergence of some relaxed parallel multisplitting methods. By using this new result one can improve many convergence results of the related iterative methods and give very simple proofs of these results.