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Motivations for an Arbitrary Precision Interval Arithmetic and the MPFI Library

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Reliable Computing

Abstract

This paper justifies why an arbitrary precision interval arithmetic is needed. To provide accurate results, interval computations require small input intervals; this explains why bisection is so often employed in interval algorithms. The MPFI library has been built in order to fulfill this need. Indeed, no existing library met the required specifications. The main features of this library are briefly given and a comparison with a fixed-precision interval arithmetic, on a specific problem, is presented. It shows that the overhead due to the multiple precision is completely acceptable. Eventually, some applications based on MPFI are given: robotics, isolation of polynomial real roots (by an algorithm combining symbolic and numerical computations) and approximation of real roots with arbitrary accuracy.

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Authors and Affiliations

  1. INRIA, Project Arenaire, LIP (CNRS/ENSL/INRIA/UCBL), École Normale Supérieure de Lyon, 69364, Lyon Cedex 07, France

    Nathalie Revol

  2. Salsa Project, INRIA Rocquencourt and LIP6, France

    Fabrice Rouillier

Authors
  1. Nathalie Revol
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  2. Fabrice Rouillier
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Correspondence to Nathalie Revol.

Additional information

This work was done while N. Revol was a member of the ANO Laboratory, University of Lille, France, on sabbatical leave within the Arenaire project.

This work was done while F. Rouillier belonged to the Spaces project, LORIA and LIP6, France.

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Revol, N., Rouillier, F. Motivations for an Arbitrary Precision Interval Arithmetic and the MPFI Library. Reliable Comput 11, 275–290 (2005). https://doi.org/10.1007/s11155-005-6891-y

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  • DOI: https://doi.org/10.1007/s11155-005-6891-y

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