Interval Representations

R.H.N. Santiago, B.R.C Bedregal, B.M. Acióly

Abstract


This paper presents the concept of interval representation and shows some of its properties. The concept is often applied in interval mathematics and captures the essence of that theory; namely: Interval analysis is a language that designates computations with real numbers. The idea of interval objects as representation of real objects is defined and its relation with some aspects of interval analysis is showed. Some of these relations are concerned with the topological aspects of intervals (Scott topology).

References


[1] B.M. Acióly and B.R.C. Bedregal, A quasi-metric topology compatible with inclusion monotonicity on interval space, Reliable Computing, 3, No. 3 (1997), 305-313.

B.M. Acióly, “Computational foundations of interval mathematics”, Ph.D. thesis, in Portuguese, Instituto de informática, Universidade Federal do Rio Grande do Sul, Dezembro 1991.

E. Loh and G.W. Walster, Rump’s example revisited, Reliable Computing, 8, No. 3 (2002), 245-248.

A. McCluskey and B. McMaster, “Topology Course Lecture Notes”, Topology Atlas, 1999. Available in http://at.yorku.ca/i/a/a/b/23.htm.

R.E. Moore, “Methods and applications of interval analysis”, SIAM Studies in Applied and Numerical Methematics, SIAM, 1979.

E. Novak, The real number model in numerical analysis, Journal of Complexity, 11, No. 1 (1995), 57-73.

D. S. Scott, Outline of a mathematical theory of computation, in “4th Princeton Conference on Information Science and Systems”, pp. 65-106, 1970.

J. Stoy, “Denotational semantics: The Scott-Strachey approach to programming language theory”, MIT Press, Massachusetts, 1977.

K. Weihrauch, “Computable analysis - an introduction”, Springer Verlag, 1997.




DOI: https://doi.org/10.5540/tema.2004.05.02.0317

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Trends in Computational and Applied Mathematics

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