Study of the dynamics of third-order iterative methods on quadratic polynomials
comunitat-uji-handle:10234/9
comunitat-uji-handle2:10234/7037
comunitat-uji-handle3:10234/8635
comunitat-uji-handle4:
INVESTIGACIONMetadata
Title
Study of the dynamics of third-order iterative methods on quadratic polynomialsDate
2012Publisher
Taylor & FrancisISSN
0020-7160; 1029-0265Bibliographic citation
International Journal of Computer Mathematics Volume 89, Issue 13-14, 2012 Special Issue: COMPUTATIONAL AND MATHEMATICAL METHODS IN SCIENCE AND ENGINEERINGType
info:eu-repo/semantics/articleVersion
info:eu-repo/semantics/sumittedVersionSubject
Abstract
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 ... [+]
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. [-]
Is part of
International Journal of Computer Mathematics, 2012,vol. 89, núm. 13-14Rights
© Informa UK Limited, an Informa Group Company
This is an Author's Original Manuscript of an article submitted for consideration in the INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS [copyright Taylor & Francis]; INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS is available online at http://www.tandfonline.com/10.1080/00207160.2012.687446
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info:eu-repo/semantics/openAccess
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- MAT_Articles [766]