Miller Analyzer for Matlab: A Matlab Package for Automatic Roundoff Analysis

Abstract

We give a first report on our new software, Miller Analyzer for Matlab, which is an automatic roundoff error analyzer that extends the work of Miller et al. Using the original work of Miller, the analyzed numerical algorithm had to be expressed in a special, greatly simplified programming language. The main disadvantage of Miller's software is its own programming language and its restrictions. We have eliminated this drawback by creating a Matlab interface to the method of Miller. Applying the operator overloading based implementation technique of automatic differentiation, we have provided a means of analyzing numerical methods given in the form of Matlab m-functions. This new way of defining the analyzed numerical method is more flexible, and the integration into the Matlab environment makes the use of the software easy. Our work can be useful in analyzing the numerical stability of algorithms that use only the four basic real (not complex) arithmetic operations and square root. At the end of the paper, we discuss two such examples.