Abstract

Computational differentiation is a means of finding the first, second, and higher order partial derivatives of a function. Computational differentiation eliminates the truncation error of numerical differentiation and reduces the roundoff error that often accompanies numerical differentiation. Computational differentiation provides the accuracy of analytical derivatives but does not require the user to find the analytical expressions. MATLAB is a software package oriented around vector and matrix operations. The latest version of MATLAB provides objects and operator overloading. These two features make it particularly attractive for implementing computational differentiation. A basic library of computational derivative routines is presented as MATLAB M-fils. A nonlinear optimization M-file based on Newton's method is given and applied to logit, probit, and ordered probit models as examples.

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