An Algorithm for Solving Non-Linear Equations Based on the Secant Method

Abstract

This paper describes a variant of the generalized secant method for solving simultaneous nonlinear equations. The method is of particular value in cases where the evaluation of the residuals for imputed values of the unknowns is tedious, or a good approximation to the solution and the Jacobian at the solution are available. Experiments are described comparing the method with the Newton–Raphson process. It is shown that for suitable problems the method is considerably superior.