A fast reliable iteration method for dc analysis of nonlinear networks

Abstract

A new iteration method for nonlinear dc analysis, based on Broyden's modification of the Newton-Raphson method, is described. Broyden introduces a variable correction factor which is chosen so as to minimize, or at least reduce, the size of the error vector at each iteration. This completely precludes divergence of the algorithm. Broyden also develops a means for updating the inverse Jacobian matrix without ever having to compute or invert it explicitly. Two algorithms are described, one for solving a single nonlinear problem and the other for solving a large number of neighboring problems such as are encountered in statistical (Monte Carlo) analysis. Timing measurements on these two algorithms are reported. Application of these algorithms to statistical ac analysis and to frequency response calculations is proposed and a possible method of improving the basic algorithm by means of a sparse matrix technique is described.