Regions of convergence and dynamics of Schröder-like iteration formulae as applied to complex polynomial equations with multiple roots

DOI10.1007/s11075-019-00806-7zbMath1450.65043OpenAlexW2980243929MaRDI QIDQ2192576

Takemitsu Hasegawa, Tomohiro Suzuki, Sugiura, Hiroshi

Publication date: 17 August 2020

Published in: Numerical Algorithms (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11075-019-00806-7

zbMATH Keywords

basin of attractionVoronoi diagramalgebraic equationroot findingSchröder's methodcircles of Apollonius

Mathematics Subject Classification ID

Numerical computation of solutions to single equations (65H05) Numerical computation of roots of polynomial equations (65H04)

Related Items (1)

The link on extraneous non-repelling cycles of Schröder's methods of the first and second kind

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Polynomial root-finding methods whose basins of attraction approximate Voronoi diagram
• Extraneous fixed points, basin boundaries and chaotic dynamics for Schröder and König rational iteration functions
• On extraneous fixed-points of the basic family of iteration functions
• Dynamic study of Schröder's families of first and second kind
• Dynamics and limiting behavior of Julia sets of König's method for multiple roots
• Estimating convergence regions of Schröder's iteration formula: how the Julia set shrinks to the Voronoi boundary
• A class of iterative methods for holomorphic functions
• On Schröder's families of root-finding methods
• Numerical Computing with IEEE Floating Point Arithmetic
• On the Julia set of König’s root–finding algorithms
• Complex analytic dynamics on the Riemann sphere
• Generalized Computation of Schröder Iteration Functions To Motivate Families of Julia and Mandelbrot-Like Sets
• On K nig's root-finding algorithms*

This page was built for publication: Regions of convergence and dynamics of Schröder-like iteration formulae as applied to complex polynomial equations with multiple roots