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Numerical methods for nonlinear equations

Published online by Cambridge University Press:  04 May 2018

C. T. Kelley
C. T. Kelley*
Affiliation:
Department of Mathematics, North Carolina State University, Raleigh, NC 27695-8205, USA E-mail: tim_kelley@ncsu.edu
*
*E-mail: tim_kelley@ncsu.edu
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Abstract

This article is about numerical methods for the solution of nonlinear equations. We consider both the fixed-point form $\mathbf{x}=\mathbf{G}(\mathbf{x})$ and the equations form $\mathbf{F}(\mathbf{x})=0$ and explain why both versions are necessary to understand the solvers. We include the classical methods to make the presentation complete and discuss less familiar topics such as Anderson acceleration, semi-smooth Newton’s method, and pseudo-arclength and pseudo-transient continuation methods.

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Research Article
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Acta Numerica , Volume 27 , 01 May 2018 , pp. 207 - 287
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© Cambridge University Press, 2018 

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