Inexact block Newton methods for solving nonlinear equations

Abstract

In the paper two parallelizable inexact block Newton methods are presented for solving large and sparse nonlinear equations. The basic idea is simple and direct. Combining the simplified Newton method with the component averaging (CAV) method [Parallel Comput. 27 (2001) 777] results in an inexact Newton method, called simplified Newton-CAV method. Parallel tests of the algorithm are implemented on a message-passing distributed-memory multiprocessor architecture such as a cluster of workstations. The results show that the new algorithm can achieve good performance. Moreover as a development of the simplified Newton-CAV method, the overlapped block Newton-CAV method is further proposed and discussed.