Method for Solving Non-Linear Simultaneous Equations Using the Gradient Vectors

摘要

Occasionally, it becomes necessary to solve a complicated set of non-linear simultaneous equations. The problem may arise when those design parameters are sought which must satisfy a number of non-linear restraint or when the maxima or minima of a non-linear function are required. The stationary values of such a function are given by the values of the variables which make the partial derivatives of the function vanish. These solutions usually are difficult to obtain by simple means, and one can not always be certain that other solutions in the range of interest are not being overlooked. In this note, methods using the gradient vectors are developed for solving the non-linear simultaneous equations f(x,y) = g(x,y) = O and also the equations f(x,y,z) = g(x,y,z) = h(x,y,z) = O. (Author)