New subclasses of block H-matrices with applications to parallel decomposition-type relaxation methods

Abstract

The parallel decomposition-type relaxation methods for solving large sparse systems of linear equations on SIMD multiprocessor systems have been proposed in [3] and [2]. In case when the coefficient matrix of the linear system is a block H-matrix, sufficient conditions for the convergence of methods given in [2], [3] have been further improved in [5] and [4]. From the practical point of view, the convergence area obtained there is not always suitable for computation, so we propose new, easily computable ones, for some special subclasses of block H-matrices. Furthermore, this approach improves the already known convergence area for the class of block strictly diagonally dominant (SDD) matrices. © Springer Science+Business Media B.V. 2006.