ON THE MONOTONE CONVERGENCE OF MULTISPLITTING METHOD FOR A CLASS OF SYSTEMS OF WEAKLY NONLINEAR EQUATIONS

In this paper, we set up a parallel matrix multisplitting iterative me thod for a class of system of weakly nonlinear equations, Au = G(u), A is an element of L(R(n)), G:R(n) --> R(n), which is generally resulte d from the discretization of many classical differential equations. Fo r the new method, the two-sided approximation property is deliberately shown, and the comparison theorems between the convergence rates of d ifferent multisplittings as well as multisplitting and single splittin gs of the coefficient matrix A is an element of L(R(n)) are given in d etail in the sense of monotonicity. Therefore, the monotone convergenc e theory about this method is thoroghly established. Finally, we apply the built conclusions to several special but very important and pract ical multisplittings to confirm the correctness and effectiveness of o ur theory.