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

Abstract

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

Keywords

• Large nonlinear systems of equations
• Limited memory Broyden method
• Singular values thresholding
• Rank reduction
• Superlinear convergence.