Nonstationary multisplittings with general weighting matrices for mildly nonlinear systems

In this paper, we present a new nonstationary multisplitting iterative method for solving the mildly nonlinear equations Ax = F(x), where A ∈ Rn×n is an n-by-n sparse real symmetric positive definite matrix and F : Rn → Rn is a general nonlinear mapping, and establish the convergence theories with general weighting matrices by more than one inner iteration. Meanwhile, we also give the lower bound of the inner iteration number in this nonstationary multisplitting iterative method.