A New Broyden rank reduction method to solve large systems of nonlinear equations

Abstract

We propose a modification of limited memory Broyden methods, called dy-namical Broyden rank reduction method, to solve high dimensional systems ofnonlinear equations. Based on a thresholding process of singular values, theproposed method determines a priori the rank of the reduced update matrix.It significantly reduces the number of singular values decomposition calls ofthe update matrix during the iterations. Local superlinear convergence of themethod is proved and some numerical examples are displayed.