Convergence and comparison theorems for a generalized alternating iterative method

Using as a principal tool the convergence results of standard iterative process for the solution of linear systems, alternating iterative methods are studied. We extend the convergence theorem for the stationary alternating iterative method of Benzi and Szyld [Numererische Mathematik 76 (1997) 309], for weak nonnegative splittings of the first type of a monotone matrix to weak nonnegative splitting of the second type. On the other hand, we introduce a more general method, the nonstationary alternating iterative method, establishing convergence results for weak nonnegative splittings of a monotone matrix, and for P-regular splittings of a symmetric positive definite matrix. (C) 2002 Elsevier Science Inc. All rights reserved.