Solving an ill-conditioned nonlinear system of equations

This article lists a computer program in BASIC for solving an ill-conditioned nonlinear system of equations in the literature. Computational results are also presented here. Unlike the author's earlier publications, in which the penalty function is the sum of the absolute values of the residuals, and in an attempt to make the worst residuals more dominant over the better residuals, the present article uses the penalty function of the sum of the squares of the residuals. With this change, improving the value of the newer penalty function is now more like lust improving the values of the worse residuals; the result is that all residuals of a solution tend to be more uniform in size. (C) 1998 John Wiley & Sons, Inc.