NEWTON'S VERSUS HALLEY'S METHOD: A DYNAMICAL SYSTEMS APPROACH

DOI10.1142/S0218127404011399zbMath1129.37332MaRDI QIDQ4655729

Jeremy Horgan-Kobelski, Gareth E. Roberts

Publication date: 8 March 2005

Published in: International Journal of Bifurcation and Chaos (Search for Journal in Brave)

zbMATH Keywords

Newton's methoddynamical systemsHalley's methodMandelbrot-like sets

Mathematics Subject Classification ID

Numerical computation of solutions to single equations (65H05) Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets (37F10) Dynamical systems in numerical analysis (37N30)

Related Items

A construction of attracting periodic orbits for some classical third-order iterative methods ⋮ Third-degree anomalies of Traub's method ⋮ Effective numerical methods for non-linear equations ⋮ Superattracting extraneous fixed points and \(n\)-cycles for Chebyshev's method on cubic polynomials ⋮ A complex dynamical approach of Chebyshev's method ⋮ Analysis of optimal iterative methods from a dynamical point of view by studying their stability properties ⋮ The ``Gauss-Seidelization of iterative methods for solving nonlinear equations in the complex plane ⋮ On the local convergence of Kung-Traub's two-point method and its dynamics. ⋮ A first overview on the real dynamics of Chebyshev's method ⋮ Some variants of the Chebyshev–Halley family of methods with fifth order of convergence ⋮ Singular perturbations ofzⁿwith a pole on the unit circle ⋮ On the dynamics of a family of third-order iterative functions ⋮ On the dynamics of some Newton's type iterative functions ⋮ Measures of the Basins of Attracting n-Cycles for the Relaxed Newton’s Method ⋮ Newton Method and Trajectory-Based Method for Solving Power Flow Problems: Nonlinear Studies

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the iteration of a rational function: Computer experiments with Newton's method
• Extraneous fixed points, basin boundaries and chaotic dynamics for Schröder and König rational iteration functions
• Complex analytic dynamics on the Riemann sphere
• On the Convergence of Halley's Method
• On the Geometry of Halley's Method
• Julia sets for the super-Newton method, Cauchy’s method, and Halley’s method
• The Dynamics of Newton's Method for Cubic Polynomials