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Paper 36

On the Behavior of Chebyshev's Method applied to Cubic Polynomials

Á.A. Magreñán¹, M. García-Olivo² and J.M. Gutiérrez³

¹Departamento de TFG/TFM, Universidad Internacional de La Rioja, Spain
²Área de Ciencias Básicas y Ambientales, Instituto Tecnológico de Santo Domingo, Dominican Republic
³Departamento de Matemáticas y Computación, Universidad de La Rioja, Spain

doi:10.4203/ccp.105.36

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, "On the Behavior of Chebyshev's Method applied to Cubic Polynomials", in , (Editors), "Proceedings of the Ninth International Conference on Engineering Computational Technology", Civil-Comp Press, Stirlingshire, UK, Paper 36, 2014. doi:10.4203/ccp.105.36

Keywords: Chebyshev's method, real dynamics, convergence plane, cubic polynomials.

Summary

This paper shows the dynamical behavior of the well-known Chebyshev method when it is applied to cubic polynomials. We present the scaling theorem associated to the method and we study the real dynamics of the method. The convergence plane is used to obtain the same kind of information as from the Lyapunov exponents and Feigenbaum diagrams, and even more.

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Front Page Browse CCP CSETS CTR IJRT Other Authors Search Purchase Guide FAQ Contact us	Civil-Comp Proceedings ISSN 1759-3433 CCP: 105 PROCEEDINGS OF THE NINTH INTERNATIONAL CONFERENCE ON ENGINEERING COMPUTATIONAL TECHNOLOGY Edited by: Paper 36 On the Behavior of Chebyshev's Method applied to Cubic Polynomials Á.A. Magreñán¹, M. García-Olivo² and J.M. Gutiérrez³ ¹Departamento de TFG/TFM, Universidad Internacional de La Rioja, Spain ²Área de Ciencias Básicas y Ambientales, Instituto Tecnológico de Santo Domingo, Dominican Republic ³Departamento de Matemáticas y Computación, Universidad de La Rioja, Spain doi:10.4203/ccp.105.36 purchase the full-text of this paper Full Bibliographic Reference for this paper , "On the Behavior of Chebyshev's Method applied to Cubic Polynomials", in , (Editors), "Proceedings of the Ninth International Conference on Engineering Computational Technology", Civil-Comp Press, Stirlingshire, UK, Paper 36, 2014. doi:10.4203/ccp.105.36 Keywords: Chebyshev's method, real dynamics, convergence plane, cubic polynomials. Summary This paper shows the dynamical behavior of the well-known Chebyshev method when it is applied to cubic polynomials. We present the scaling theorem associated to the method and we study the real dynamics of the method. The convergence plane is used to obtain the same kind of information as from the Lyapunov exponents and Feigenbaum diagrams, and even more. purchase the full-text of this paper (price £20) go to the previous paper go to the next paper return to the table of contents return to the book description purchase this book (price £45 +P&P)
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