SSOR and ASSOR preconditioners for Block-Broyden method

Solving nonlinear equations is a problem that needs to be dealt with in the practical engineering application. This paper uses Block–Broyden method for solving large-scale nonlinear systems, and two preconditioners are applied for solving the underlying linear systems, including SSOR preconditioner as well as ASSOR method, which is based on SSOR. It discusses their implementation processes and compares the two algorithms from different aspects. Finally, it solves the nonlinear systems arising from the Bratu problem. Experimental results show that the preconditioning technique is effective for the Block–Broyden method and that the preconditioner ASSOR has better performance as a whole. Therefore, it can be used in the large-scale problems arising from scientific and engineering computing. 2006 Elsevier Inc. All rights reserved.