Polynomial root-finding methods whose basins of attraction approximate Voronoi diagram

DOI10.1007/s00454-011-9330-3zbMath1221.65111OpenAlexW2021586346MaRDI QIDQ542397

Bahman Kalantari

Publication date: 10 June 2011

Published in: Discrete \& Computational Geometry (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00454-011-9330-3

zbMATH Keywords

Newton's methoddynamical systemscomplex polynomialszerosJulia setVoronoi diagramcomputational geometryfractaliteration functionspolynomial root-finding

Mathematics Subject Classification ID

Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral) (30C15) General theory of numerical methods in complex analysis (potential theory, etc.) (65E05) Numerical computation of roots of polynomial equations (65H04)

Related Items

Dynamics and limiting behavior of Julia sets of König's method for multiple roots, Mollified Zone Diagrams and Their Computation, Regions of convergence and dynamics of Schröder-like iteration formulae as applied to complex polynomial equations with multiple roots, Algorithms for quaternion polynomial root-finding, Polynomial and rational approximations and the link between Schröder's processes of the first and second kind, Newton–Ellipsoid polynomiography, Estimating convergence regions of Schröder's iteration formula: how the Julia set shrinks to the Voronoi boundary

Cites Work

• Families of rational maps and iterative root-finding algorithms
• On extraneous fixed-points of the basic family of iteration functions
• Mollified Zone Diagrams and Their Computation
• Zone Diagrams: Existence, Uniqueness, and Algorithmic Challenge
• Dynamics in One Complex Variable. (AM-160)
• Generalization of Taylor's theorem and Newton's method via a new family of determinantal interpolation formulas and its applications
• A determinantal lower bound
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