1An Efficient Overloaded Method for Computing Derivatives of Mathematical Functions in MATLAB

An object-oriented method is presented that computes without truncation error derivatives of functions defined by MATLAB computer codes. The method implements forward mode automatic differentiation via operator overloading in a manner that produces a new MATLAB code which computes the derivatives of the outputs of the original function with respect to the variables of differentiation. Because the derivative code has the same input as the original function code, the method can be used recursively to generate derivatives of any order that are desired. In addition, the approach developed in this paper has the feature that the derivatives are generated simply by evaluating the function on an instance of the class, thus making the method straightforward to use while simultaneously enabling differentiation of highly complex functions. A detailed description of the method is presented and the approach is illustrated and is shown to be efficient on four examples