A small probabilistic universal set of starting points for finding roots of complex polynomials by Newton’s method

DOI10.1090/S0025-5718-2012-02640-8zbMath1283.37043arXiv1009.1843OpenAlexW2963199029MaRDI QIDQ4911911

Béla Bollobás, Dierk Schleicher, Malte Lackmann

Publication date: 20 March 2013

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1009.1843

zbMATH Keywords

Newton's methodroots of complex polynomialsstarting point

Mathematics Subject Classification ID

Newton-type methods (49M15) Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets (37F10)

Related Items (10)

A bias in the volatility smile ⋮ The Weierstrass–Durand–Kerner root finder is not generally convergent ⋮ Dynamics and limiting behavior of Julia sets of König's method for multiple roots ⋮ Newton's method in practice. II: The iterated refinement Newton method and near-optimal complexity for finding all roots of some polynomials of very large degrees ⋮ Finding polynomial roots by dynamical systems -- a case study ⋮ On the speed of convergence of Newton’s method for complex polynomials ⋮ Combinatorial properties of Newton maps ⋮ On the efficient global dynamics of Newton’s method for complex polynomials ⋮ Diverging orbits for the Ehrlich–Aberth and the Weierstrass root finders ⋮ Newton's method in practice: finding all roots of polynomials of degree one million efficiently

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• On the efficiency of algorithms of analysis
• Dynamics in One Complex Variable. (AM-160)
• On the efficient global dynamics of Newton’s method for complex polynomials
• How to find all roots of complex polynomials by Newton's method.

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