Influence of the multiplicity of the roots on the basins of attraction of Newton's method

DOI10.1007/S11075-013-9742-7zbMath1296.65072OpenAlexW2076562985MaRDI QIDQ398582

Miguel Marañon Grandes, Maria Teresa Rivas Rodriguez, José Manuel Gutiérrez Jimenez, Louis Javier Hernandez Paricio

Publication date: 15 August 2014

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

Full work available at URL: https://doi.org/10.1007/s11075-013-9742-7

zbMATH Keywords

Newton's methodbasin of attractionnumerical resultmeasure algorithmsmultiplicity of a rootsubdivisions on the sphere

Mathematics Subject Classification ID

Numerical computation of roots of polynomial equations (65H04)

Related Items (6)

PARAMETER ESTIMATION OF THE CLASSICAL FRACTAL MAP BASED ON A GIVEN JULIA SET’S SHAPE ⋮ Self-overlays and symmetries of Julia sets of expanding maps ⋮ The shape of the Julia set of an expanding rational map ⋮ Graphical representations for the homogeneous bivariate Newton's method ⋮ Bivariate Newton-Raphson method and toroidal attraction basins ⋮ Measures of the Basins of Attracting n-Cycles for the Relaxed Newton’s Method

Uses Software

• Healpix

Cites Work

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• Plotting basins of end points of rational maps with Sage
• Julia sets of Newton's method for a class of complex-exponential function \(F(z)=P(z)e^{Q(z)}\)
• Symmetries of the Julia sets of Newton's method for multiple root
• Graphic and numerical comparison between iterative methods
• Cayley's problem and Julia sets
• The complex dynamics of Newton's method for a double root
• The Julia set of Newton's method for multiple root
• Julia sets for the standard Newton's method, Halley's method, and Schröder's method
• Julia sets of the Schröder iteration functions of a class of one-parameter polynomials with high degree
• Limit and end functors of dynamical systems via exterior spaces
• Convergence and Applications of Newton-type Iterations
• JULIA SETS OF GENERALIZED NEWTON'S METHOD
• JULIA SET OF THE NEWTON TRANSFORMATION FOR SOLVING SOME COMPLEX EXPONENTIAL EQUATION

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