On the speed of convergence of Newton’s method for complex polynomials

DOI10.1090/mcom/2985zbMath1333.37018arXiv1202.2475OpenAlexW1580887024MaRDI QIDQ2792334

Todor Bilarev, Dierk Schleicher, Magnus Aspenberg

Publication date: 9 March 2016

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

Full work available at URL: https://arxiv.org/abs/1202.2475

Mathematics Subject Classification ID

Newton-type methods (49M15) Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets (37F10) Numerical problems in dynamical systems (65P99)

Related Items (11)

ON THE DISTANCE TO A ROOT OF COMPLEX POLYNOMIALS UNDER NEWTON'S METHOD ⋮ The Weierstrass–Durand–Kerner root finder is not generally convergent ⋮ 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 ⋮ Geometry of polynomials and root-finding via path-lifting ⋮ Finding polynomial roots by dynamical systems -- a case study ⋮ A small probabilistic universal set of starting points for finding roots of complex polynomials by Newton’s method ⋮ Puzzles and the Fatou–Shishikura injection for rational Newton maps ⋮ 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

Cites Work

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• The maximum-entropy measure of a rational endomorphism of the Riemann sphere
• Newton's method in practice: finding all roots of polynomials of degree one million efficiently
• A small probabilistic universal set of starting points for finding roots of complex polynomials by Newton’s method
• Complex Dynamics, the Mandelbrot Set, and Newton’s Method — or: On Useless and Useful Mathematics
• How to find all roots of complex polynomials by Newton's method.

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