Parallel multisplitting two-stage iterative methods with general weighting matrices for non-symmetric positive definite systems

In this work, we propose a new parallel multisplitting iterative method for non-symmetric positive definite linear systems. Based on optimization theory, the new method has two great improvements; one is that only one splitting needs to be convergent, and the other is that the weighting matrices are not scalar and nonnegative matrices. The convergence of the new parallel multisplitting iterative method is discussed. Finally, the numerical results show that the new method is effective.