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The Complex Dynamics of Newton’s Method

Wiersma, A.G. (2016) The Complex Dynamics of Newton’s Method. Bachelor's Thesis, Mathematics.

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Abstract

Newton's method is the best known iteration method for finding a real or a complex root. When the function f(x) has more than one root, which root Newton's method finds depends on the initial guess. This leads to an interesting pattern even for polynomials. We can even expand this to the complex plane by using the function f(z) of a complex number z. The behavior of Newton's method for these functions leads to interesting fractal patterns. We will look at how these fractal patterns emerge for several polynomial and trigonometric functions. Furthermore we will compare the dynamics of Newton's method with the relaxed Newton's method and the Secant method.

Item Type: Thesis (Bachelor's Thesis)
Degree programme: Mathematics
Thesis type: Bachelor's Thesis
Language: English
Date Deposited: 15 Feb 2018 08:14
Last Modified: 15 Feb 2018 08:14
URI: http://fse.studenttheses.ub.rug.nl/id/eprint/14180

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