AN APPLICATION OF THE METHOD OF STEEPEST DESCENTS TO THE SOLUTION OF SYSTEMS OF NON-LINEAR SIMULTANEOUS EQUATIONS

Abstract

The solution of non-linear simultaneous equations using the ‘method of steepest descents’ is discussed. A comparison is made with the Southwell and Synge procedures for the solution of a set of equations, and it is concluded that the proposed method requires only about 1/n times the number of ‘steps’ to reach a solution. It is emphasized, however, that in view of the rather complicated expressions which must be calculated, it is best suited for use in conjunction with a high-speed electronic computer Finally a method is given for discriminating between real and false solutions in the case when the problem is one of minimization rather than of obtaining an exact solution.