Convergence behaviors of multisplitting methods with relaxed parameters

In this paper, two multisplitting methods with K + 1 relaxed parameters are established for solving a linear system whose coefficient matrix is a large sparse M -matrix or H -matrix and the corresponding convergence behaviors are studied. Then the implementation of these two methods with ILU factorizations as inner splittings is investigated. Finally, some numerical experiments are presented to illustrate the effectiveness of the preconditioners obtained from our methods when combined with BiCGSTAB.