Block and asynchronous two-stage methods for mildly nonlinear systems

Block parallel iterative methods for the solution of mildly nonlinear syste ms of equations of the form Ax = Phi(x) are studied. Two-stage methods, whe re the solution of each block is approximated by an inner iteration, are tr eated. Both synchronous and asynchronous versions are analyzed, and both po intwise and blockwise convergence theorems provided. The case where there a re overlapping blocks is also considered. The analysis of the asynchronous method when applied to linear systems includes cases not treated before in the literature. Mathematics Subject Classification (1991): 65H10, 65F10.