Generalized inverse methods for the best least squares solution of systems of non-linear equations

Abstract

It is shown how many previous methods for the exact solution (or best least squares solution) of systems of non-linear equations are all based upon simple cases of the generalized inverse of the matrix of first derivatives of the equations. The general case is given and algorithms for its application are suggested, especially in the case where the matrix of first derivatives cannot be calculated. Numerical tests confirm that these algorithms extend the range of practical problems which can be solved.