Splitting iterations for circulant-plus-diagonal systems

Abstract

We consider the system of linear equations (C + iD)x = b, where C is a circulant matrix and D is a real diagonal matrix. We study the technique for constructing the normal/skew-Hermitian splitting for such coefficient matrices. Theoretical results show that if the eigenvalues of C have positive real part, the splitting method converges to the exact solution of the system of linear equations. When the eigenvalues of C have non-negative real part, the convergence conditions are also given. We present a successive overrelaxation acceleration scheme for the proposed splitting iteration. Numerical examples are given to illustrate the effectiveness of the method. Copyright © 2005 John Wiley & Sons, Ltd.