Tutorial: abstraction in numerical methods

Authors:
Gerald Jay Sussman;Matthew Halfant
Affiliations:
Artificial Intelligence Laboratory and Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology;Artificial Intelligence Laboratory and Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology
Venue:
LFP '88 Proceedings of the 1988 ACM conference on LISP and functional programming
Year:
1988

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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.