Inexact overlapped block Broyden methods for solving nonlinear equations

摘要

In this paper a parallelizable overlapped block Broyden method is presented for solving large systems of nonlinear equations. The basic idea is to perform the block Broyden iteration described in [SIAM J. Sci. Comput. 18 (1997) 1367] for the overlapped blocks and then assemble the overlapping solutions in a weighted average manner at each iteration. A family of nonlinear overlapped solvers could be generated combining it with some iterative or direct linear solvers. The conditions under which the algorithm is locally convergent are studied and many useful techniques regarding the implementation are also considered.