Study of the dynamics of third-order iterative methods on quadratic polynomials
In this paper, we analyse the dynamical behaviour of the operators associated with multi-point interpolation iterative methods and frozen derivative methods, for solving nonlinear equations, applied on second-degree complex polynomials. We obtain that, in both cases, the Julia set is connected and s...
| Authors: | , , |
|---|---|
| Format: | article |
| Publication Date: | 2012 |
| Country: | España |
| Institution: | Universitat Politècnica de València (UPV) |
| Repository: | RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia |
| Language: | English |
| OAI Identifier: | oai:riunet.upv.es:10251/55273 |
| Online Access: | https://riunet.upv.es/handle/10251/55273 |
| Access Level: | Open access |
| Keyword: | Nonlinear equations Iterative methods Complex dynamics Conjugacy map Basin of attraction MATEMATICA APLICADA |
| Summary: | In this paper, we analyse the dynamical behaviour of the operators associated with multi-point interpolation iterative methods and frozen derivative methods, for solving nonlinear equations, applied on second-degree complex polynomials. We obtain that, in both cases, the Julia set is connected and separates the basins of attraction of the roots of the polynomial. Moreover, the Julia set of the operator associated with multi-point interpolation methods is the same as the Newton operator, although it is more complicated for the frozen derivative operator. We explain these differences by obtaining the conjugacy function of each method and by showing that the operators associated with Newton's method and multi-point interpolation methods are both conjugate to powers of z. |
|---|