Second-Derivative-Free Variant of the Chebyshev Method for Nonlinear Equations

Keywords

Mathematics, Lipschitz continuity, Derivative (finance), Chebyshev iteration, Chebyshev filter

References

• Nondiscrete induction and iterative processesFlorian A. Potra, Vlastimil Pták — 1984
• Computational Methods in Ordinary Differential EquationsJ. D. Lambert — 1973
• Solution of equations and systems of equationsE. I., Alexander Ostrowski — 1967
• Iterative Methods for the Solution of EquationsDavid M. Young, J. F. Traub — 1982
• A family of chebyshev type methods in banach spacesM. A. Hernádez, M. A. Salanova — 1996
• The Kantorovich Theorem for Newton's MethodR. A. Tapia — 1971
• Iterative solution of nonlinear equationsR. D. Murphy — 1994
• Einige Sätze über das Verfahren der tangierenden Hyperbeln in Banach-RäumenBoro Döring — 1970
• Results on the Chebyshev method in banach spacesIoannis K. Argyros, Dong Chen — 1993
• The Kantorovich Theorem for Newton's MethodR. A. Tapia — 1971
• Toward a Unified Convergence Theory for Newton-Like MethodsJ. Dennis — 1971

Cited by

• Familias paramétricas de procesos iterativos de alto orden de convergenciaNatalia Romero Álvarez — 2006
• Ball convergence comparison between three iterative methods in Banach space under hypothese only on the first derivativeIoannis K. Argyros, Santhosh George — 2015
• ON THE CONVERGENCE OF INEXACT TWO-STEP NEWTON-TYPE METHODS USING RECURRENT FUNCTIONSIoannis K. Argyros, Said Hilou — 2011
• CONVERGENCE BEHAVIOR FOR NEWTON-STEFFENSEN'S METHOD UNDER LIPSCHITZ CONDITION OF SECOND DERIVATIVEShaohua Yu, Xiubin Xu, Jianqiu Li — 2011
• HIGH-ORDER NEWTON-KRYLOV METHODS TO SOLVE SYSTEMS OF NONLINEAR EQUATIONSM.T. Darvishi, Byeong‐Chun Shin — 2011
• Sixth-order and Seventh-order Iterative Methods for Solving Nonlinear EquationsFayyaz Ahmad, Domingo Garcı́a-Senz — 2013
• Some Third Order Methods for Solving Systems of Nonlinear EquationsJanak Raj Sharma, Rajni Sharma — 2011
• Semilocal convergence of multi-point improved super-Halley-type methods without the second derivative under generalized weak conditionXiuhua Wang, Jisheng Kou — 2016
• Convergence analysis on a class of improved Chebyshev methods for nonlinear equations in Banach spacesXiuhua Wang, Jisheng Kou — 2015
• Semilocal convergence of a family of third-order Chebyshev-type methods under a mild differentiability conditionP. K. Parida, D. K. Gupta — 2010
• The convergence theorem for a family deformed Chebyshev method in Banach spaceQingbiao Wu, Yueqing Zhao — 2006
• Recurrence relations for semilocal convergence of a Newton-like method in Banach spacesP. K. Parida, D. K. Gupta — 2008
• Constructing third-order derivative-free iterative methodsSanjay Kumar Khattri, Torgrim Log — 2011
• Some second-derivative-free variants of Chebyshev-Halley methodsChangbum Chun — 2007
• Traub-type high order iterative procedures on Riemannian manifoldsSergio Amat, Ioannis K. Argyros, Sonia Busquier — 2014
• Highly efficient classes of Chebyshev-Halley type methods free from second-order derivativeRamandeep Behl, V. Kanwar — 2014
• A Stirling-like method with Hölder continuous first derivative in Banach spacesSanjaya Kumar Parhi, Divyansh Gupta — 2011
• Convergence for a class of multi-point modified Chebyshev-Halley methods under the relaxed conditionsXiuhua Wang, Jisheng Kou — 2015
• Derivative free algorithm for solving nonlinear equationsSanjay Kumar Khattri, Torgrim Log — 2011
• On Chebyshev‐type methods free from second derivativeJisheng Kou, Yitian Li — 2007

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