Performance analysis of preconditioners based on Broyden method

Solving nonlinear equations is a problem often needed to be dealt with in the practical engineering application. This paper discusses preconditioning methods based on Block Broyden method. It first introduces the Block Broyden method and preconditioning technique. Then it presents four different preconditioners for the Block Broyden method and discusses the implementation process. It also analyzes the time complexity of the four algorithms. Finally, it solves the nonlinear systems arising from the Bratu problem by the four preconditioning algorithms. Experimental results show that the preconditioning technique is effective for the Block Broyden method and that the preconditioner SSOR has the fastest solving speed and the best performance among the four preconditioners. Therefore, it can be used in the large-scale problems arising from scientific and engineering computing.