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International Journal of Computer Mathematics Volume 47, 1993 - Issue 1-2
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Original Articles

A family of chebyshev-halley type methods

M. A. Hernández Colegio Universitario de la Rioja, C/ Obispo Bustamante 3, Logroño, 26001, Spain
&
M. A. Salanova Colegio Universitario de la Rioja, C/ Obispo Bustamante 3, Logroño, 26001, Spain
Pages 59-63 | Published online: 19 Mar 2007

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B. Campos, Alicia Cordero, Juan R. Torregrosa & P. Vindel. (2015) Dynamics of the family of c-iterative methods. International Journal of Computer Mathematics 92:9, pages 1815-1825.
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J. A. Ezquerro, J. M. Gutiérrez & M. A. Hernández. (1998) Solving a nonlinear equation by a uniparametric family of iterative processes. International Journal of Computer Mathematics 68:3-4, pages 301-308.
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J.M. Gutiérrez, M.A. Hernández & M.A. Salanova. (1996) Resolution of quadratic equations in banach spaces. Numerical Functional Analysis and Optimization 17:1-2, pages 113-121.
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M. A. Hernádez & M. A. Salanova. (1996) A family of chebyshev type methods in banach spaces. International Journal of Computer Mathematics 61:1-2, pages 145-154.
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M. A. Hernández & M. A. Salanova. (1994) A family of newton type iterative processes. International Journal of Computer Mathematics 51:3-4, pages 205-214.
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Articles from other publishers (37)

José M. Gutiérrez & Víctor Galilea. (2023) Two Dynamic Remarks on the Chebyshev–Halley Family of Iterative Methods for Solving Nonlinear Equations. Axioms 12:12, pages 1114.
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Sapan Kumar Nayak, P. K. Parida & Abhimanyu Kumar. (2023) A study of 3$$\mu $$th-order of convergence of Chebyshev–Halley family method and its convergence plane. SeMA Journal.
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Rosendo Monroy-Loperena. (2023) An efficient, robust and reliable initialization of phase fractions in Rachford-Rice system of equations for three-phase split calculation. Fluid Phase Equilibria 566, pages 113690.
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Xiaofeng Wang & Ying Cao. (2023) A numerically stable high-order Chebyshev-Halley type multipoint iterative method for calculating matrix sign function. AIMS Mathematics 8:5, pages 12456-12471.
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Stoil I. Ivanov. (2022) Unified Convergence Analysis of Chebyshev–Halley Methods for Multiple Polynomial Zeros. Mathematics 10:1, pages 135.
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Sergio Amat, Rodrigo Castro, Gerardo Honorato & Á. A. Magreñán. (2020) Purely Iterative Algorithms for Newton’s Maps and General Convergence. Mathematics 8:7, pages 1158.
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Santhosh George & Ioannis K Argyros. (2019) Extending the radius of convergence for a class of Euler-Halley type methods. Journal of Numerical Analysis and Approximation Theory 48:2, pages 137-143.
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Wartono .M. Soleh, I. Suryani, Zulakmal .Muhafzan .. (2018) A New Variant of Chebyshev-Halley’s Method Without Second Derivative with Convergence of Optimal Order. Asian Journal of Scientific Research 11:3, pages 409-414.
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S. Amat & S. Busquier. (2017) After notes on Chebyshev’s iterative method. Applied Mathematics and Nonlinear Sciences 2:1, pages 1-12.
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Beatriz Campos, Alicia Cordero, Juan R. Torregrosa & Pura Vindel. (2016) Dynamics of a multipoint variant of Chebyshev–Halley’s family. Applied Mathematics and Computation 284, pages 195-208.
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Diyashvir Kreetee Rajiv Babajee. (2014) On a two-parameter Chebyshev-Halley-like family of optimal two-point fourth order methods free from second derivatives. Afrika Matematika 26:5-6, pages 689-697.
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Gerardo Honorato & Sergio Plaza. (2015) Dynamical aspects of some convex acceleration methods as purely iterative algorithm for Newton’s maps. Applied Mathematics and Computation 251, pages 507-520.
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Rongfei Lin, Yueqing Zhao, Qingbiao Wu & Jueliang Hu. (2014) Convergence Theorem for a Family of New Modified Halley’s Method in Banach Space. Journal of Applied Mathematics 2014, pages 1-8.
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B. Campos, A. Cordero, Á. A. Magreñán, J. R. Torregrosa & P. Vindel. (2014) Study of a Biparametric Family of Iterative Methods. Abstract and Applied Analysis 2014, pages 1-12.
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Trond Steihaug & Sara Suleiman. (2013) Rate of convergence of higher order methods. Applied Numerical Mathematics 67, pages 230-242.
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Alicia Cordero, Juan R. Torregrosa & Pura Vindel. (2013) Dynamics of a family of Chebyshev–Halley type methods. Applied Mathematics and Computation 219:16, pages 8568-8583.
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Yonghui Ling, Xiubin Xu & Shaohua Yu. (2013) Convergence Behavior for Newton-Steffensen’s Method under -Condition of Second Derivative. Abstract and Applied Analysis 2013, pages 1-11.
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J.M. McNamee & V.Y. Pan. 2013. Numerical Methods for Roots of Polynomials - Part II. Numerical Methods for Roots of Polynomials - Part II 215 379 .
Jin-Hua Wang. (2010) Convergence Criterion of the Family of Euler-Halley Type Methods for Sections on Riemannian Manifolds. Taiwanese Journal of Mathematics 14:6.
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Huang Zhengda & Ma Guochun. (2009) On the local convergence of a family of Euler-Halley type iterations with a parameter. Numerical Algorithms 52:3, pages 419-433.
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Jin-Hua Wang & Chong Li. (2009) CONVERGENCE OF THE FAMILY OF EULER-HALLEY TYPE METHODS ON RIEMANNIAN MANIFOLDS UNDER THE $\gamma$-CONDITION. Taiwanese Journal of Mathematics 13:2A.
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S. Amat, S. Busquier, J.M. Gutiérrez & M.A. Hernández. (2008) On the global convergence of Chebyshev's iterative method. Journal of Computational and Applied Mathematics 220:1-2, pages 17-21.
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Naoki Osada. (2008) Chebyshev–Halley methods for analytic functions. Journal of Computational and Applied Mathematics 216:2, pages 585-599.
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Ioannis K. Argyros. (2007) On the convergence of Newton's method for a class of nonsmooth operators. Journal of Computational and Applied Mathematics 205:1, pages 584-593.
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Xintao Ye, Chong Li & Weiping Shen. (2007) Convergence of the variants of the Chebyshev–Halley iteration family under the Hölder condition of the first derivative. Journal of Computational and Applied Mathematics 203:1, pages 279-288.
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Sergio Amat, Sonia Busquier & Sergio Plaza. (2009) On the dynamics of a family of third-order iterative functions. The ANZIAM Journal 48:3, pages 343-359.
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. 2007. Computational Theory of Iterative Methods. Computational Theory of Iterative Methods 457 482 .
Ioannis K. Argyros. (2006) On the Secant method for solving nonsmooth equations. Journal of Mathematical Analysis and Applications 322:1, pages 146-157.
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Xintao Ye & Chong Li. (2006) Convergence of the family of the deformed Euler–Halley iterations under the Hölder condition of the second derivative. Journal of Computational and Applied Mathematics 194:2, pages 294-308.
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S. Amat, Sonia Busquier & S. Plaza. (2006) A construction of attracting periodic orbits for some classical third-order iterative methods. Journal of Computational and Applied Mathematics 189:1-2, pages 22-33.
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J.M. Gutiérrez & M.A. Hernández. (1998) Recurrence relations for the super-Halley method. Computers & Mathematics with Applications 36:7, pages 1-8.
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J.A. Ezquerro & M.A. Hernández. (1998) Avoiding the computation of the second Fréchet-derivative in the convex acceleration of Newton's method. Journal of Computational and Applied Mathematics 96:1, pages 1-12.
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J.A. Ezquerro, J.M. Gutiérrez & M.A. Hernández. (1998) A construction procedure of iterative methods with cubical convergence II: Another convergence approach. Applied Mathematics and Computation 92:1, pages 59-68.
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Ioannis K. Argyros. (1998) Improving the order and rates of convergence for the Super-Halley method in Banach spaces. Korean Journal of Computational & Applied Mathematics 5:2, pages 465-474.
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JoséM. Gutiérrez & Miguel A. Hernández. (1997) Third-order iterative methods for operators with bounded second derivative. Journal of Computational and Applied Mathematics 82:1-2, pages 171-183.
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J.A. Ezquerro, J.M. Gutiérrez & M.A. Hernández. (1997) A construction procedure of iterative methods with cubical convergence. Applied Mathematics and Computation 85:2-3, pages 181-199.
Crossref
J.M. Gutiérrez & M.A. Hernández. (2009) A family of Chebyshev-Halley type methods in Banach spaces. Bulletin of the Australian Mathematical Society 55:1, pages 113-130.
Crossref

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