Abstract
We present a local as well as a semilocal convergence analysis for some iterative algorithms in order to approximate a locally unique solution.
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References
S. Amat, S. Busquier, Third-order iterative methods under Kantorovich conditions. J. Math. Anal. Appl. 336, 243–261 (2007)
S. Amat, S. Busquier, S. Plaza, Chaotic dynamics of a third-order Newton-like method. J. Math. Anal. Appl. 366(1), 164–174 (2010)
G. Anastassiou, Fractional Differentiation Inequalities (Springer, New York, 2009)
G. Anastassiou, Intelligent Mathematics: Computational Analysis (Springer, Heidelberg, 2011)
G. Anastassiou, I. Argyros, A convergence analysis for some iterative algorithms with applications to fractional calculus, submitted (2015)
I.K. Argyros, Newton-like methods in partially ordered linear spaces. J. Approx. Theory Appl. 9(1), 1–10 (1993)
I.K. Argyros, Results on controlling the residuals of perturbed Newton-like methods on Banach spaces with a convergence structure. Southwest J. Pure Appl. Math. 1, 32–38 (1995)
I.K. Argyros, Convergence and Applications of Newton-Like Iterations (Springer, New York, 2008)
K. Diethelm, The Analysis of Fractional Differential Equations. Lecture Notes in Mathematics, vol. 2004, 1st edn. (Springer, New York, 2010)
J.A. Ezquerro, J.M. Gutierrez, M.A. Hernandez, N. Romero, M.J. Rubio, The Newton method: from Newton to Kantorovich (Spanish). Gac. R. Soc. Mat. Esp. 13, 53–76 (2010)
J.A. Ezquerro, M.A. Hernandez, Newton-like methods of high order and domains of semilocal and global convergence. Appl. Math. Comput. 214(1), 142–154 (2009)
L.V. Kantorovich, G.P. Akilov, Functional Analysis in Normed Spaces (Pergamon Press, New York, 1964)
A.A. Magrenan, Different anomalies in a Jarratt family of iterative root finding methods. Appl. Math. Comput. 233, 29–38 (2014)
A.A. Magrenan, A new tool to study real dynamics: the convergence plane. Appl. Math. Comput. 248, 215–224 (2014)
F.A. Potra, V. Ptak, Nondiscrete Induction and Iterative Processes (Pitman, London, 1984)
P.D. Proinov, New general convergence theory for iterative processes and its applications to Newton-Kantorovich type theorems. J. Complex. 26, 3–42 (2010)
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Anastassiou, G.A., Argyros, I.K. (2016). Iterative Algorithms and Left-Right Caputo Fractional Derivatives. In: Intelligent Numerical Methods: Applications to Fractional Calculus. Studies in Computational Intelligence, vol 624. Springer, Cham. https://doi.org/10.1007/978-3-319-26721-0_14
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DOI: https://doi.org/10.1007/978-3-319-26721-0_14
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