Diverging orbits for the Ehrlich–Aberth and the Weierstrass root finders

DOI10.1090/proc/15715OpenAlexW3096098241MaRDI QIDQ5027172

Bernhard Reinke

Publication date: 4 February 2022

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2011.01660

zbMATH Keywords

Weierstrassroot-finding methodEhrlich-Aberthdiverging orbitsDurand-Kerner

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Dynamical systems in numerical analysis (37N30) Numerical computation of roots of polynomial equations (65H04) Higher-dimensional holomorphic and meromorphic dynamics (37F80)

Related Items

The Weierstrass–Durand–Kerner root finder is not generally convergent, Fast Cauchy sum algorithms for polynomial zeros and matrix eigenvalues, 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, Accelerated subdivision for clustering roots of polynomials given by evaluation oracles, On the efficient global dynamics of Newton’s method for complex polynomials

Uses Software

• Maxima
• SageMath
• SINGULAR

Cites Work

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• How to find all roots of complex polynomials by Newton's method.