On the monotone convergence of multisplitting method for a class of systems of weakly nonlinear equations

Abstract

In this paper, we set up a parallel matrix multisplitting iterative method for a class of system of weakly nonlinear equations, Au = G(u), A∊L(R ⁿ), G:R ⁿ →R ⁿ , which is generally resulted from the discretization of many classical differential equations. For the new method, the two-sided approximation property is deliberately shown, and the comparison theorems between the convergence rates of different multisplit-tings as well as multisplitting and single splittings of the coefficient matrix A∊L(R ⁿ ) are given in detail in the sense of monotonicity. Therefore, the monotone convergence theory about this method is thoroghly established. Finally, we apply the built conclusions to several special but very important and practical multisplittings to confirm the correctness and effectiveness of our theory.

Keywords:

• System of weakly nonlinear equations
• Matrix multisplitting
• Monotone convergence
• Convergence rate

AMS(MOS)Subject Classifications:

• 65F10
• 65H20

C.R.Categories:

• G.1.3