Newton’s Method for Complex Polynomials: Cayley’s Problem

Heinz-Otto Peitgen and Peter H. Richter
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Heinz-Otto Peitgen: Universität Bremen, Fachbereich Mathematik
Peter H. Richter: Universität Bremen, Fachbereich Physik

Chapter 6 in The Beauty of Fractals, 1986, pp 93-102 from Springer

Abstract: Abstract Newton’s method and its sophisticated variants are among the most prominent numerical methods for finding solutions of nonlinear equations. The theory of these methods is usually presented in two parts, one with emphasis on the proof of convergence of the method, the other addressing the derivation of the asymptotic speed of convergence. The picture which one thus obtains from the literature is, however, somewhat incomplete. There are additional interesting and deep problems connected with Newton’s method one of which is the subject of the following discussion.

Keywords: Complex Polynomial; Asymptotic Speed; Liouville Number; Binary Decomposition; Sophisticated Variant (search for similar items in EconPapers)
Date: 1986
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DOI: 10.1007/978-3-642-61717-1_6

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