Lazy Functional Algorithms for Exact Real Functionals (1998)
| Venue: | Lec. Not. Comput. Sci |
| Citations: | 32 - 0 self |
BibTeX
@INPROCEEDINGS{Simpson98lazyfunctional,
author = {Alex K. Simpson},
title = {Lazy Functional Algorithms for Exact Real Functionals},
booktitle = {Lec. Not. Comput. Sci},
year = {1998},
pages = {456--464},
publisher = {Springer}
}
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Abstract
. We show how functional languages can be used to write programs for real-valued functionals in exact real arithmetic. We concentrate on two useful functionals: definite integration, and the functional returning the maximum value of a continuous function over a closed interval. The algorithms are a practical application of a method, due to Berger, for computing quantifiers over streams. Correctness proofs for the algorithms make essential use of domain theory. 1 Introduction In exact real number computation, infinite representations of reals are employed to avoid the usual rounding errors that are inherent in floating point computation [4--6, 17]. For certain real number computations that are highly sensitive to small variations in the input, such rounding errors become inordinately large and the use of floating-point algorithms can lead to completely erroneous results [1, 14]. In such situations, exact real number computation provides guaranteed correctness, although at the (probably...
Keyphrases
exact real functionals lazy functional algorithm exact real number computation guaranteed correctness usual rounding error domain theory floating-point algorithm small variation point computation useful functionals maximum value definite integration rounding error practical application certain real number computation infinite representation functional language correctness proof continuous function erroneous result real-valued functionals essential use closed interval
