After notes on Chebyshev's iterative method

• Autores: Sergio Amat Plata , Sonia Busquier Sáez
• Localización: Applied Mathematics and Nonlinear Sciences, ISSN-e 2444-8656, Vol. 2, Nº. 1, 2017, págs. 1-12
• Idioma: español
• DOI: 10.21042/amns.2017.3.00048
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• Resumen

  • This paper is a small review of Chebyshev's method. The geometric interpretation as a generalization of Newton's method is derived. Using this interpretation its global convergence is proved. Some dynamical properties are studied. As a higher order method, they are more complicated than in Newton's method. Finally, some applications are revisited pointing out the advantages of Chebyshev's method with respect Newton's method.