Practical Quasi-Newton algorithms for singular nonlinear systems

Quasi-Newton methods for solving singular systems of nonlinear equations are considered in this paper. Singular roots cause a number of problems in implementation of iterative methods and in general deteriorate the rate of convergence. We propose two modifications of QN methods based on Newton’s and Shamanski’s method for singular problems. The proposed algorithms belong to the class of two-step iterations. Influence of iterative rule for matrix updates and the choice of parameters that keep iterative sequence within convergence region are empirically analyzed and some conclusions are obtained.