A CONVERGENCE THEOREM ON AN EXTRAPOLATED ITERATIVE METHOD AND ITS APPLICATIONS

The elementary, but very useful, concept of the extrapolation or relax ation is generally used to accelerate iterative methods for solving li near systems, but its convergence conditions were not studied thorough ly. In this note a new result on the convergence of an extrapolated it erative method is derived. As its applications we discuss the converge nce of some relaxed parallel multisplitting methods. By using this new result one can improve many convergence results of the related iterat ive methods and give very simple proofs of these results. (C) 1998 Els evier Science B.V. and IMACS. All rights reserved.