The complex dynamics of Newton's method for a double root

DOI10.1016/0898-1221(91)90198-DzbMath0753.65039MaRDI QIDQ1192176

William J. Gilbert

Publication date: 27 September 1992

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

zbMATH Keywords

linear fractional transformationRiemann spheredouble rootiterationsrelaxed Newton's methodroots of a cubic

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 solutions to single equations (65H05)

Related Items (10)

The Julia set of Newton's method for multiple root ⋮ A new tool to study real dynamics: the convergence plane ⋮ GENERALIZATIONS OF NEWTON'S METHOD ⋮ Julia sets for the standard Newton's method, Halley's method, and Schröder's method ⋮ Are there any Julia sets for the Laguerre iteration function? ⋮ Influence of the multiplicity of the roots on the basins of attraction of Newton's method ⋮ JULIA SETS OF GENERALIZED NEWTON'S METHOD ⋮ Dynamical analysis on cubic polynomials of damped Traub's method for approximating multiple roots ⋮ Julia sets of Newton's method for a class of complex-exponential function \(F(z)=P(z)e^{Q(z)}\) ⋮ Effect of stochastic noise on superior Julia sets

Cites Work

• Unnamed Item
• Newton's method and complex dynamical systems
• Complex analytic dynamics on the Riemann sphere

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