TENSOLVE: A Software Package for Solving Systems of Nonlinear Equations and Nonlinear Least Squares Problems Using Tensor Methods

Abstract

This paper describes a modular software package for solving systems of nonlinear equations and nonlinear least squares problems, using a new class of methods called tensor methods. It is intended for small to medium{sized problems, say with up to 100 equations and unknowns, in cases where it is reasonable to calculate the Jacobian matrix or approximate it by nite diierences at each iteration. The software allows the user to select between a tensor method and a standard method based upon a linear model. The tensor method approximates F(x) by a quadratic model, where the second-order term is chosen so that the model is hardly more expensive to form, store, or solve than the standard linear model. Moreover, the software provides two diierent global strategies, a line search and a two-dimensional trust region approach. Test results indicate that, in general, tensor methods are signiicantly more eecient and robust than standard methods on small and medium{sized problems in iterations and function evaluations.

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