Efficient algorithms for verified scientific computing: Numerical linear algebra using interval arithmetic

Hong Diep Nguyen 1
1 ARENAIRE - Computer arithmetic
Inria Grenoble - Rhône-Alpes, LIP - Laboratoire de l'Informatique du Parallélisme
Abstract : Interval arithmetic is a means to compute verified results. However, a naive use of interval arithmetic does not provide accurate enclosures of the exact results. Moreover, interval arithmetic computations can be time-consuming. We propose several accurate algorithms and efficient implementations in verified linear algebra using interval arithmetic. Two fundamental problems are addressed, namely the multiplication of interval matrices and the verification of a floating-point solution of a linear system. For the first problem, we propose two algorithms which offer new tradeoffs between speed and accuracy.For the second problem, which is the verification of the solution of a linear system, our main contributions are twofold. First, we introduce a relaxation technique, which reduces drastically the execution time of the algorithm. Second, we propose to use extended precision for few, well-chosen parts of the computations, to gain accuracy without losing much in term of execution time.
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https://hal-ens-lyon.archives-ouvertes.fr/ensl-00560188
Contributor : Hong Diep Nguyen <>
Submitted on : Thursday, January 27, 2011 - 3:39:20 PM
Last modification on : Thursday, January 17, 2019 - 3:16:03 PM

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Hong Diep Nguyen. Efficient algorithms for verified scientific computing: Numerical linear algebra using interval arithmetic. 2011. ⟨ensl-00560188⟩

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