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Real dynamics for damped Newton's method applied to cubic polynomials

Journal of Computational and Applied Mathematics (2015) 275 527-538
DOI: 10.1016/j.cam.2013.11.019
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Abstract

In this paper we study the real dynamics of the damped Newton's methods applied to cubic polynomials, but instead of taking a value of the damping factor λ∈(0,1), we consider all values of λ∈R. The method for unusual values of λ presents different behaviors such as convergence to n-cycles or even chaos.

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Magreñán, Á. A., & Gutiérrez, J. M. (2015). Real dynamics for damped Newton’s method applied to cubic polynomials. Journal of Computational and Applied Mathematics, 275, 527–538. https://doi.org/10.1016/j.cam.2013.11.019

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