On the global convergence of Chebyshev's iterative method |
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Authors: | S Amat S Busquier JM Gutirrez MA Hernndez |
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Institution: | aDepartamento de Matemática Aplicada y Estadística, Universidad Politécnica de Cartagena, Spain;bDepartamento de Matemáticas y Computación, Universidad de La Rioja, Spain |
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Abstract: | In A. Melman, Geometry and convergence of Euler's and Halley's methods, SIAM Rev. 39(4) (1997) 728–735] the geometry and global convergence of Euler's and Halley's methods was studied. Now we complete Melman's paper by considering other classical third-order method: Chebyshev's method. By using the geometric interpretation of this method a global convergence theorem is performed. A comparison of the different hypothesis of convergence is also presented. |
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Keywords: | Nonlinear equations Iterative methods Geometry global convergence |
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