Interval Arithmetic and Standardization

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Interval Arithmetic and Standardization
Interval arithmetic is arithmetic for continuous sets. Floating-point intervals are intervals of real numbers with floating-point bounds. Operations for intervals can be efficiently implemented. Hence, the time is ripe for standardization. In this paper we present an interval model that is mathematically sound and closed for the 4 basic operations. The model allows for exception free interval arithmetic, if we carefully distinguish between clean and reliable interval arithmetic on one side and rounded floating-point arithmetic on the other side. Elementary functions for intervals can be defined. In some application areas loose evaluation of functions, i.e. evaluation over an interval which is not completely contained in the function domain, is recommended, In this case, however, a discontinuity flag has to be set to inform that Brouwer's fixed point theorem is no longer applicable. 1 Real Interval Arithmetic
Jürgen Wolff von Gudenberg
Added 29 Oct 2010
Updated 29 Oct 2010
Type Conference
Year 2008
Authors Jürgen Wolff von Gudenberg
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