Applying symbolic formula manipulation to the problem of non-linear least squares

Abstract

Symbolic formulation manipulation is a computer technique for manipulation of equations while still in symbolic form. For example, a symbolic formula manipulator is capable of differentiating X 2 to obtain 2 X. This technique has been applied to the non-linear least-squares problem, and the resulting computer program is discussed in this paper. The fitting function is entered as data and all associated derivatives are obtained symbolically within the program. The program then proceeds to evaluate the functions and derivatives as required to obtain the least-squares estimates of the unknown parameters of the fitting function. For a given set of experimental data, the user can try a wide variety of fitting functions and compare goodness-of-fit. He thus has a sophisticated tool for performing a complex statistical analysis of his data without getting bogged down in the details.