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Computing with Intervals

Yves Papegay
Organization: INRIA Sophia Antipolis, COPRIN
David Daney
Organization: INRIA Sophia Antipolis, COPRIN

2007 Wolfram Technology Conference
Conference location

Champaign, IL


Intervals have been considered by mathematicians for a while, in the study of numerical functions and numerical analysis, But only in the 1960s Moore had the Idea of replacing real numbers by intervals in computations and to study the resulting alternative arithmetics. In the last few decades, it has been used for achieving certified computations, but more surprisingly by numericians designing a lot of methods and algorithms for root finding, systems solving, local and global optimization, etc. Even if they are not yet widely implemented nor well known, these methods have shown their efficiency by succeeding on some challenging problems.

In Mathematica, a basic interval arithmetic is implemented. A few classical interval analysis algorithms, namely an extension of the Newton method for one variable root finding, are also available in MathSource in the NumericalMath`IntervalRoots` package. An extensive interface to a powerful C++ library of interval analysis was presented at the Wolfram Technology Conference 2005 by the authors.

*Wolfram Technology

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ComputingwithIntervals.nb (927.5 KB) - Mathematica Notebook [for Mathematica 6.0]