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 non-linear 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.