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Some Notes on a Method for Proving Inequalities by Computer

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Abstract

In this article we consider mathematical fundamentals of one method for proving inequalities by computer, based on the Remez algorithm. Using the well-known results of undecidability of the existence of zeros of real elementary functions, we demonstrate that the considered method generally in practice becomes one heuristic for the verification of inequalities. We give some improvements of the inequalities considered in the theorems for which the existing proofs have been based on the numerical verifications of Remez algorithm.

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Authors and Affiliations

  1. Faculty of Electrical Engineering, University of Belgrade, Bulevar Kralja Aleksandra 73, 11000, Belgrade, Serbia

    Bojan Banjac, Milica Makragić & Branko Malešević

  2. Faculty of Technical Sciences, University of Novi Sad, Trg Dositeja Obradovića 6, 21000, Novi Sad, Serbia

    Bojan Banjac

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  1. Bojan Banjac
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  2. Milica Makragić
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  3. Branko Malešević
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Correspondence to Branko Malešević.

Additional information

Research is partially supported by the Ministry of Science and Education of the Republic of Serbia, Grants ON 174032 and III 44006.

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Banjac, B., Makragić, M. & Malešević, B. Some Notes on a Method for Proving Inequalities by Computer. Results. Math. 69, 161–176 (2016). https://doi.org/10.1007/s00025-015-0485-8

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