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.