Study of the dynamics of third-order iterative methods on quadratic polynomials
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Publication:4903474
DOI10.1080/00207160.2012.687446zbMath1255.37019OpenAlexW2085276782MaRDI QIDQ4903474
Pura Vindel, Alicia Cordero, Juan Ramón Torregrosa Sánchez
Publication date: 22 January 2013
Published in: International Journal of Computer Mathematics (Search for Journal in Brave)
Full work available at URL: http://hdl.handle.net/10234/64512
Numerical computation of solutions to single equations (65H05) Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets (37F10)
Related Items (8)
Third-degree anomalies of Traub's method ⋮ Local convergence of a family of iterative methods for Hammerstein equations ⋮ Newton-Kantorovich convergence theorem of a new modified Halley's method family in a Banach space ⋮ Unnamed Item ⋮ Dynamics of a family of Chebyshev-Halley type methods ⋮ Recurrence relations for a family of iterations assuming Hölder continuous second order Fréchet derivative ⋮ Enlarging the convergence domain in local convergence studies for iterative methods in Banach spaces ⋮ Newton-Kantorovich and Smale uniform type convergence theorem for a deformed Newton method in Banach spaces
Cites Work
- On the iteration of a rational function: Computer experiments with Newton's method
- Iterative methods for use with nonlinear discrete algebraic models
- A construction of attracting periodic orbits for some classical third-order iterative methods
- Dynamics of a new family of iterative processes for quadratic polynomials
- On interpolation variants of Newton's method for functions of several variables
- Some variant of Newton's method with third-order convergence.
- Some new variants of Newton's method.
- Chaotic dynamics of a third-order Newton-type method
- Attracting cycles for the relaxed Newton's method
- On the dynamics of the Euler iterative function
- Multi-Point Iterative Methods for Systems of Nonlinear Equations
- On the dynamics of polynomial-like mappings
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