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Verification methods: Rigorous results using floating-point arithmetic

Published online by Cambridge University Press:  10 May 2010

Siegfried M. Rump
Siegfried M. Rump
Affiliation:
Institute for Reliable Computing, Hamburg University of Technology, Schwarzenbergstraße 95, 21071 Hamburg, Germany and Visiting Professor at Waseda University, Faculty of Science and Engineering, 3–4–1 Okubo, Shinjuku-ku, Tokyo, 169–8555, Japan, E-mail: rump@tu-harburg.de
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A classical mathematical proof is constructed using pencil and paper. However, there are many ways in which computers may be used in a mathematical proof. But ‘proof by computer’, or even the use of computers in the course of a proof, is not so readily accepted (the December 2008 issue of the Notices of the American Mathematical Society is devoted to formal proofs by computer).

In the following we introduce verification methods and discuss how they can assist in achieving a mathematically rigorous result. In particular we emphasize how floating-point arithmetic is used.

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Research Article
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Acta Numerica , Volume 19 , May 2010 , pp. 287 - 449
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Copyright © Cambridge University Press 2010

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