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On the number of iterations of Newton's method for complex polynomials

Published online by Cambridge University Press:  19 June 2002

DIERK SCHLEICHER
DIERK SCHLEICHER
Affiliation:
School of Engineering and Science, International University Bremen, Postfach 750561, D-28725 Bremen, Germany (e-mail: [email protected])
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Abstract

We use methods from conformal geometry to give an explicit estimate for how many iterations of Newton's method it takes, at most, to find all the roots of an arbitrary complex polynomial of fixed degree with prescribed precision.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 22 , Issue 3 , June 2002 , pp. 935 - 945
Copyright
2002 Cambridge University Press

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