Tutorial: abstraction in numerical methods

Abstract

We illustrate how the liberal use of high-order procedural abstractions and infinite streams helps us to express some of the vocabulary and methods of numerical analysis. We develop a software toolbox encapsulating the technique of Richardson extrapolation, and we apply these tools to the problems of numerical integration and differentiation. By separating the idea of Richardson extrapolation from its use in particular circumstances we indicate how numerical programs can be written that exhibit the structure of the ideas from which they are formed.