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Numerical Algorithms for the Parametric Continuation of Stiff ODEs Deriving from the Modeling of Combustion with Detailed Chemical Mechanisms Read chapter Read first chapter

2020 | OriginalPaper | Chapter

Generalizations of the Intermediate Value Theorem for Approximating Fixed Points and Zeros of Continuous Functions

Author : Michael N. Vrahatis

Published in: Numerical Computations: Theory and Algorithms

Publisher: Springer International Publishing

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Abstract

Generalizations of the traditional intermediate value theorem are presented. The obtained generalized theorems are particular useful for the existence of solutions of systems of nonlinear equations in several variables as well as for the existence of fixed points of continuous functions. Based on the corresponding criteria for the existence of a solution emanated by the intermediate value theorems, generalized bisection methods for approximating fixed points and zeros of continuous functions are given. These bisection methods require only algebraic signs of the function values and are of major importance for tackling problems with imprecise (not exactly known) information.

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previous chapter In the Quest for Invariant Structures Through Graph Theory, Groups and Mechanics: Methodological Aspects in the History of Applied Mathematics
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Metadata
Title
Generalizations of the Intermediate Value Theorem for Approximating Fixed Points and Zeros of Continuous Functions
Author
Michael N. Vrahatis
Copyright Year
2020
Book
Numerical Computations: Theory and Algorithms

Print ISBN: 978-3-030-40615-8

Electronic ISBN: 978-3-030-40616-5

Copyright Year: 2020

DOI
https://doi.org/10.1007/978-3-030-40616-5_17

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