research-article

Fast and Parallel Interval Arithmetic

Author:

Siegfried M. RumpAuthors Info & Claims

Volume 39, Issue 3

Pages 534 - 554

https://doi.org/10.1023/A:1022374804152

Published: 01 September 1999 Publication History

Abstract

Infimum-supremum interval arithmetic is widely used because of ease of implementation and narrow results. In this note we show that the overestimation of midpoint-radius interval arithmetic compared to power set operations is uniformly bounded by a factor 1.5 in radius. This is true for the four basic operations as well as for vector and matrix operations, over real and over complex numbers. Moreover, we describe an implementation of midpoint-radius interval arithmetic entirely using BLAS. Therefore, in particular, matrix operations are very fast on almost any computer, with minimal effort for the implementation. Especially, with the new definition it is seemingly the first time that full advantage can be taken of the speed of vector and parallel architectures. The algorithms have been implemented in the Matlab interval toolbox INTLAB.

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Cited By

Wicker MPatane ALaurenti LKwiatkowska M(2024)Adversarial Robustness Certification for Bayesian Neural NetworksFormal Methods10.1007/978-3-031-71162-6_1(3-28)Online publication date: 9-Sep-2024
https://dl.acm.org/doi/10.1007/978-3-031-71162-6_1
Nikas IGrapsa T(2020)Hybridization of bisection method for solving non-differentiable nonlinear equationsProceedings of the 24th Pan-Hellenic Conference on Informatics10.1145/3437120.3437324(277-280)Online publication date: 20-Nov-2020
https://dl.acm.org/doi/10.1145/3437120.3437324
Minamihata AOgita TRump SOishi S(2020)Modified error bounds for approximate solutions of dense linear systemsJournal of Computational and Applied Mathematics10.1016/j.cam.2019.112546369:COnline publication date: 1-May-2020
https://dl.acm.org/doi/10.1016/j.cam.2019.112546
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cover image BIT

BIT Volume 39, Issue 3

Sep 1999

200 pages

ISSN:0006-3835

Issue’s Table of Contents

Copyright © 1999 Swets & Zeitlinger.

Publisher

BIT Computer Science and Numerical Mathematics

United States

Publication History

Published: 01 September 1999

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Cited By

Wicker MPatane ALaurenti LKwiatkowska M(2024)Adversarial Robustness Certification for Bayesian Neural NetworksFormal Methods10.1007/978-3-031-71162-6_1(3-28)Online publication date: 9-Sep-2024
https://dl.acm.org/doi/10.1007/978-3-031-71162-6_1
Nikas IGrapsa T(2020)Hybridization of bisection method for solving non-differentiable nonlinear equationsProceedings of the 24th Pan-Hellenic Conference on Informatics10.1145/3437120.3437324(277-280)Online publication date: 20-Nov-2020
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Minamihata AOgita TRump SOishi S(2020)Modified error bounds for approximate solutions of dense linear systemsJournal of Computational and Applied Mathematics10.1016/j.cam.2019.112546369:COnline publication date: 1-May-2020
https://dl.acm.org/doi/10.1016/j.cam.2019.112546
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Nguyen HRevol N(2010)High performance linear algebra using interval arithmeticProceedings of the 4th International Workshop on Parallel and Symbolic Computation10.1145/1837210.1837236(171-172)Online publication date: 21-Jul-2010
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