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2016 | OriginalPaper | Chapter

2. Solving A Nonlinear Equation

Author : Mark H. Holmes

Published in: Introduction to Scientific Computing and Data Analysis

Publisher: Springer International Publishing

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Abstract

In this chapter one of the more common mathematical problems is studied, which is to find the solution, or solutions, of an equation of the form f(x) = 0. To illustrate the situation, we begin with a few examples.

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Boyd, J.P.: Solving Transcendental Equations: The Chebyshev Polynomial Proxy and Other Numerical Rootfinders, Perturbation Series, and Oracles. Other Titles in Applied Mathematics. SIAM, Philadelphia (2014). ISBN 9781611973525. https://books.google.com/books?id=29CgBAAAQBAJ CrossRefMATH

Cordero, A., Jordnn, C., Torregrosa, J.R.: One-point Newton-type iterative methods: a unified point of view. J. Comput. Appl. Math. 275, 366–374 (2015). ISSN 0377-0427. doi:http://dx.doi.org/10.1016/j.cam.2014.07.009. http://www.sciencedirect.com/science/article/pii/S0377042714003288

Dennis, J.E., Jr., Schnabel, R.B.: Numerical Methods for Unconstrained Optimization and Nonlinear Equations. SIAM, Philadelphia, PA (1996). ISBN 0898713641CrossRefMATH

Fourier, M.: Analyse des Équations Déterminées. Paris, Didot (1831). https://books.google.com/books?id=HIU_AAAAcAAJ

Holmes, M.H.: Introduction to the Foundations of Applied Mathematics. Springer, New York (2009)CrossRefMATH

Johnson, K.A., Goody, R.S.: The original Michaelis constant: translation of the 1913 Michaelis-Menten paper. Biochemistry 50 (39), 8264–8269 (2011)CrossRef

Kollerstrom, N.: Thomas Simpson and ‘Newton’s method of approximation’: an enduring myth. Br. J. Hist. Sci. 25, 347–354 (1992). ISSN 1474-001X. doi:10.1017/S0007087400029150. http://journals.cambridge.org/article_S0007087400029150

Raphson, J.: Analysis Aequationum Universalis. London (1690). http://books.google.com/books?id=JM4ZuQAACAAJ

Traub, J.F.: Iterative Methods for the Solution of Equations. AMS Chelsea Publishing Series. Chelsea, New Jersey (1982). ISBN 9780828403122. http://books.google.com/books?id=se3YdgFgz4YC MATH

Wallis, J.: Operum Mathematicorum. Number v. 2. Typis Leon, Oxford (1699). http://books.google.com/books?id=dhetMBKF4gkC

White, F.M.: Viscous Fluid Flow. McGraw Hill Series in Mechanical Engineering, 3rd edn. McGraw-Hill, New York (2005)

Wilkins, G., Gu, M.: A modified Brent’s method for finding zeros of functions. Numer. Math. 123 (1), 177–188 (2013). ISSN 0029-599X. doi:10.1007/s00211-012-0480-x. http://dx.doi.org/10.1007/s00211-012-0480-x

Ypma, T.J.: Historical development of the Newton-Raphson method. SIAM Rev. 37 (4), 531–551 (1995). ISSN 0036-1445. doi:10.1137/1037125. http://dx.doi.org/10.1137/1037125

Title: Solving A Nonlinear Equation
Author: Mark H. Holmes
Publisher: Springer International Publishing
Book: Introduction to Scientific Computing and Data Analysis
Print ISBN: 978-3-319-30254-6

Electronic ISBN: 978-3-319-30256-0

Copyright Year: 2016
DOI: https://doi.org/10.1007/978-3-319-30256-0_2

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