Convergence of relaxed multisplitting USAOR methods for H-matrices linear systems

Relaxed technique is one of the techniques for improving convergence rate of splitting iterative methods. In this paper, based on the methods in Frommer and Mayer [A. Frommer, F. Mayer, Convergene of relaxed parallel multisplitting methods, Linear Algebra and its Applications 119 (1989) 141-152] and Zhang et al. [L.T. Zhang, T.Z. Huang, T.X. Gu, Global relaxed non-stationary multisplitting multi-parameters methods, International Journal of Computer Mathematics 85(2) (2008) 211-224.], we present local relaxed parallel multisplitting method, global relaxed parallel multisplitting method, local relaxed non-stationary parallel multisplitting multi-parameters method and global relaxed non-stationary parallel multisplitting multi-parameters method, and study the convergence of our methods associated with USAOR multisplitting for solving a large sparse linear system whose coefficient matrix is an H-matrix. When choosing the approximately optimal relaxed parameters, our methods have faster convergence rate, which is showed through numerical examples.