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Abstract: We start with a mathematical de nition of a real interval as a closed, connected set of reals. Interval arithmetic operations (addition, subtraction, multiplication and division) are likewise de ned mathematically and we provide algorithms for computing these operations assuming exact real arithmetic. Next, we de ne interval arithmetic operations on intervals with IEEE 754 oating point endpoints to be sound and optimal approximations of the real interval operations and we show that the IEEE... (Update)
Context of citations to this paper: More
...which has been designed with careful attention to soundness. The underlying interval arithmetic algorithms have been proved correct [14, 13], and we are preparing a proof of the correctness of the contractors for the special functions (exp, log, sin, etc. 4 Higher level...
.... to evaluate an arithmetic expression on floating point numbers is guaranteed to contain the mathematical result of that evaluation [9]. Multiple precision arithmetic is also sometimes used in Interval arithmetic systems. For example, in [10] a C toolbox is described...
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BibTeX entry: (Update)
T. Hickey, Q. Ju, and M.H. van Emden, Interval Arithmetic: from Principles to Implementation, Brandeis University Tech Report. CS-99-202, July, 1999. http://citeseer.nj.nec.com/article/hickey99interval.html More
@article{ hickey01interval,
author = "Timothy J. Hickey and Qun Ju and Maarten H. van Emden",
title = "Interval arithmetic: From principles to implementation",
journal = "Journal of the ACM",
volume = "48",
number = "5",
pages = "1038-1068",
year = "2001",
url = "citeseer.nj.nec.com/article/hickey99interval.html" }
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205 Global Optimization Using Interval Analysis (context) - Hansen - 1992
194 Introduction to Interval Computations (context) - otz, urgen - 1983
112 Rigorous Global Search: Continuous Problems (context) - Kearfott - 1996
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15 Applying interval arithmetic to real (context) - ed, Benhamou et al. - 1997
15 A more complete interval arithmetic (context) - Kahan - 1968
13 The extended real interval system - Walster - 1998
12 Experiments using interval analysis for solving a circuit de.. (context) - Ratschek, Rokne - 1993
11 Numerical Toolbox for Veried Computing (context) - Hammer, Hocks et al. - 1993
8 Interval arithmetic as a closed arithmetic system on a compu.. (context) - Hanson - 1968
7 Large-scale behaviour of junction transistors (context) - Ebers, Moll - 1954
4 Schaum's Outline Series (context) - Lipschutz - 1965
3 Theory of preconditioners for the interval Gauss-Seidel meth.. (context) - Novoa - 1993
3 On extended interval arithmetic and inclusion isotonicity (context) - Ratz - 1996
3 Topics in Interval Analysis (context) - Hansen - 1969
2 Bell-Northern Research Computing Research Laboratory (context) - Older, specication - 1989
2 Self-validated numerical methods and applications (context) - Stol, de Figueiredo - 1997
1 stands for \Never a NaN (context) - Forsythe, computation et al. - 1970
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