Are there any Julia sets for the Laguerre iteration function?

DOI10.1016/S0898-1221(03)90212-4zbMath1046.37025WikidataQ122956363 ScholiaQ122956363MaRDI QIDQ597250

Vassileios Drakopoulos

Publication date: 6 August 2004

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

zbMATH Keywords

Julia setFatou setCritical pointLaguerre's methodmicrocomputer plots

Mathematics Subject Classification ID

Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable (30D05) Small divisors, rotation domains and linearization in holomorphic dynamics (37F50) Iteration theory, iterative and composite equations (39B12) Simulation of dynamical systems (37M05) Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets (37F10)

Related Items (4)

On optimal parameter of Laguerre's family of zero-finding methods ⋮ Repellers for the Laguerre Iteration Function ⋮ Characterization of the determinant of a Laguerre matrix ⋮ On the dynamics of a family of third-order iterative functions

Cites Work

• Families of rational maps and iterative root-finding algorithms
• On the dynamics of Laguerre's iteration: \(Z^ n-1\)
• The complex dynamics of Newton's method for a double root
• Generalized Computation of Schröder Iteration Functions To Motivate Families of Julia and Mandelbrot-Like Sets
• HOW IS THE DYNAMICS OF KÖNIG ITERATION FUNCTIONS AFFECTED BY THEIR ADDITIONAL FIXED POINTS?
• Laguerre's Method Applied to the Matrix Eigenvalue Problem
• Laguere’s Method and a Circle which Contains at Least One Zero of a Polynomial
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