Concepedia

GENERALIZATIONS OF NEWTON'S METHOD

William J. Gilbert

Fractals · 2001 · 27 citations · 13 references

DOI

Concepts

Abstract

We give a survey of the complex dynamics of various generalizations of Newton's method for finding a complex root of a polynomial of a single variable.

References

13

Complex analytic dynamics on the Riemann sphere

Paul Blanchard · Bulletin of the American Mathematical Society · 1984 · 575 citations · Full text

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Families of Rational Maps and Iterative Root-Finding Algorithms

Curt McMullen · Annals of Mathematics · 1987 · 182 citations · Full text

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On the iteration of a rational function: Computer experiments with Newton's method

James H. Curry, Lucy Garnett, Dennis Sullivan · Communications in Mathematical Physics · 1983 · 164 citations

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Extraneous fixed points, basin boundaries and chaotic dynamics for Schr�der and K�nig rational iteration functions

Edward R. Vrscay, William J. Gilbert · Numerische Mathematik · 1987 · 139 citations

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Solving the quintic by iteration

Peter G. Doyle, Curt McMullen · Acta Mathematica · 1989 · 104 citations · Full text

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