Parallel Newton Iterative Methods Based on Incomplete LU Factorizations for Solving Nonlinear Systems

摘要

Parallel iterative algorithms based on the Newton method and on two of its variations, the Shamanskii method and the Chord method, for solving nonlinear systems are proposed. These algorithms also use techniques from the non-stationary multisplitting methods. Concretely, in order to construct the multisplitting, ILU factorizations are considered. Convergence properties of these parallel methods are studied for H-matrices. Computational results, on a distributed multiprocessor IBM RS/6000 SP, that show the effectiveness of these methods are included to illustrate the theoretical results.