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Survey on Generalizations of the Intermediate Value Theorem and Applications

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Computer Algebra in Scientific Computing (CASC 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13366))

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Abstract

Generalizations of the intermediate value theorem in several variables are presented. These theorems are very useful in various approaches including the existence of solutions of systems of nonlinear equations, the existence of fixed points of continuous functions as well as the existence of periodic orbits of nonlinear mappings and similarly, fixed points of the Poincaré map on a surface of section. Based on the corresponding criteria for the existence of a solution or a fixed point emanated by the intermediate value theorems, generalized bisection methods for approximating zeros or fixed points of continuous functions are given. These bisection methods require only the algebraic signs of the function values and are of major importance for studying and tackling problems with imprecise information.

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Acknowledgments

The author would like to thank the editors for their kind invitation.

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Authors and Affiliations

  1. Department of Mathematics, University of Patras, 26110, Patras, Greece

    Michael N. Vrahatis

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  1. Michael N. Vrahatis
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Correspondence to Michael N. Vrahatis .

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Editors and Affiliations

  1. Université de Lille, Villeneuve d'Ascq, France

    François Boulier

  2. Coventry University, Coventry, UK

    Matthew England

  3. Plekhanov Russian University of Economics, Moscow, Russia

    Timur M. Sadykov

  4. Institute of Theoretical and Applied Mechanics, Novosibirsk, Russia

    Evgenii V. Vorozhtsov

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Vrahatis, M.N. (2022). Survey on Generalizations of the Intermediate Value Theorem and Applications. In: Boulier, F., England, M., Sadykov, T.M., Vorozhtsov, E.V. (eds) Computer Algebra in Scientific Computing. CASC 2022. Lecture Notes in Computer Science, vol 13366. Springer, Cham. https://doi.org/10.1007/978-3-031-14788-3_1

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  • DOI: https://doi.org/10.1007/978-3-031-14788-3_1

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