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Abstract: We start with a mathematical definition of a real interval as a closed, connected set of reals. Interval arithmetic operations (addition, subtraction, multiplication and division) are likewise defined mathematically and we provide algorithms for computing these operations assuming exact real arithmetic. Next, we define interval arithmetic operations on intervals with IEEE 754 floating point endpoints to be sound and optimal approximations of the real interval operations and we show that... (Update)
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...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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207 Global Optimization Using Interval Analysis (context) - Hansen - 1992
198 Introduction to Interval Computations (context) - Alefeld, Herzberger - 1983
117 Rigorous Global Search: Continuous Problems (context) - Kearfott - 1996
39 Numerical Toolbox for Verified Computing (context) - Hammer, Hocks et al. - 1993
25 Numerica: A Modeling Language for Global Optimization - Van Hentenryck, Michel et al. - 1997
15 Applying interval arithmetic to real (context) - Benhamou, Older - 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
12 Self-validated numerical methods and applications - Stolfi, de Figueiredo - 1997
9 A constraint satisfaction approach to a circuit design probl.. - Puget, Van Hentenryck - 1998
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
4 Topics in Interval Analysis (context) - Hansen - 1969
3 On extended interval arithmetic and inclusion isotonicity (context) - Ratz - 1996
3 Theory of preconditioners for the interval Gauss-Seidel meth.. (context) - Novoa - 1993
2 Bell-Northern Research Computing Research Laboratory (context) - Older, specification - 1989
2 or why a math book isn't enough (context) - Forsythe, computation - 1970
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