Convergence theorems for parallel multisplitting two-stage iterative methods for mildly nonlinear systems

Abstract

For the system of mildly nonlinear equations Ax= F( x), where A∈ R n×n is an n-by- n sparse real matrix and F: R n→ R n a general nonlinear mapping, both local and global convergence properties of the multisplitting two-stage iterative method (Numer. Algorithms 15 (1997) 347) are further studied in depth when A∈ R n×n is symmetric positive definite and its multiple splittings are symmetric P-regular.