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International Journal of Computer Mathematics Volume 81, 2004 - Issue 9
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On the local convergence of secant-type methods

S. Amat * Departamento de Matemática Aplicada y Estadística, Universidad de Cartagena, Spain
,
S. Busquier † Departamento de Matemática Aplicada y Estadística, Universidad de Cartagena, Spain
&
J. M. Gutiérrez Departamento de Matemáticas y Computación, Universidad de La Rioja, SpainCorrespondence[email protected]
Pages 1153-1161 | Accepted 28 Mar 2004, Published online: 25 Jan 2007

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I.K. Argyros, D. González & Á.A. Magreñán. (2014) Majorizing sequences for Newton's method under centred conditions for the derivative. International Journal of Computer Mathematics 91:12, pages 2568-2583.
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Otu Vaarmann. (2006) High order iterative methods for decomposition‐coordination problems. Ukio Technologinis ir Ekonominis Vystymas 12:1, pages 56-61.
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Articles from other publishers (28)

Samundra Regmi, Ioannis K. Argyros, Stepan Shakhno & Halyna Yarmola. (2023) Unified Convergence Criteria of Derivative-Free Iterative Methods for Solving Nonlinear Equations. Computation 11:3, pages 49.
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Gus I. Argyros, Michael I. Argyros, Samundra Regmi, Ioannis K. Argyros & Santhosh George. (2020) On the Solution of Equations by Extended Discretization. Computation 8:3, pages 69.
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Ioannis K. Argyros, Stepan Shakhno & Halyna Yarmola. (2020) Extending the Convergence Domain of Methods of Linear Interpolation for the Solution of Nonlinear Equations. Symmetry 12:7, pages 1093.
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Ioannis K. Argyros & Stepan Shakhno. (2020) Extended Two-Step-Kurchatov Method for Solving Banach Space Valued Nondifferentiable Equations. International Journal of Applied and Computational Mathematics 6:2.
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Ioannis Argyros & Stepan Shakhno. (2019) Extended Local Convergence for the Combined Newton-Kurchatov Method Under the Generalized Lipschitz Conditions. Mathematics 7:2, pages 207.
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Á. Alberto Magreñán, Ioannis K. Argyros, Lara Orcos & Juan Antonio Sicilia. (2017) Secant-like methods for solving nonlinear models with applications to chemistry. Journal of Mathematical Chemistry 56:7, pages 1935-1957.
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Á. Alberto Magreñán & Ioannis K. Argyros. 2018. A Contemporary Study of Iterative Methods. A Contemporary Study of Iterative Methods 105 133 .
Massimiliano Ferrara, Somayeh Sharifi & Mehdi Salimi. (2016) Computing multiple zeros by using a parameter in Newton–Secant method. SeMA Journal 74:4, pages 361-369.
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Abhimanyu Kumar, D. K. Gupta & Shwetabh Srivastava. (2017) Influence of the Center Condition on the Two-Step Secant Method. International Journal of Analysis 2017, pages 1-9.
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Ioannis K. Argyros & Á.Alberto MagreñánIoannis K. Argyros & Á. Alberto Magreñán. 2017. Iterative Methods and Their Dynamics with Applications. Iterative Methods and Their Dynamics with Applications 216 240 .
M.A. Hernández-Verón & M.J. Rubio. (2017) On the local convergence of a Newton–Kurchatov-type method for non-differentiable operators. Applied Mathematics and Computation 304, pages 1-9.
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IOANNIS K. ARGYROS & SANTHOSH GEORGE. (2017) A convergence of a Steffensen-like method for solving nonlinear equations in a Banach space. Creative Mathematics and Informatics 26:2, pages 125-136.
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Á. Alberto Magreñán & Ioannis K. Argyros. (2016) New improved convergence analysis for the secant method. Mathematics and Computers in Simulation 119, pages 161-170.
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Sergio Amat, Sonia Busquier, Concepción Bermúdez & Ángel Magreñán. (2015) Expanding the Applicability of a Third Order Newton-Type Method Free of Bilinear Operators. Algorithms 8:3, pages 669-679.
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Á. Alberto Magreñán & Ioannis K. Argyros. (2015) New semilocal and local convergence analysis for the Secant method. Applied Mathematics and Computation 262, pages 298-307.
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A. Alberto Magrenan & Ioannis K. Argyros. (2015) EXPANDING THE APPLICABILITY OF SECANT METHOD WITH APPLICATIONS. Bulletin of the Korean Mathematical Society 52:3, pages 865-880.
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I. K. Argyros, J. A. Ezquerro, M. A. Hernández-Verón, S. Hilout & Á. A. Magreñán. (2015) ENLARGING THE CONVERGENCE DOMAIN OF SECANT-LIKE METHODS FOR EQUATIONS. Taiwanese Journal of Mathematics 19:2.
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Á. Alberto Magreñán & Ioannis K. Argyros. (2014) Optimizing the applicability of a theorem by F. Potra for Newton-like methods. Applied Mathematics and Computation 242, pages 612-623.
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Ioannis K. Argyros & Sanjay K. Khattri. (2014) Convergence analysis for the two-step Newton method of order four. Journal of Numerical Analysis and Approximation Theory 43:1, pages 33-44.
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I. K. Argyros, D. González & Á. A. Magreñán. (2014) A Semilocal Convergence for a Uniparametric Family of Efficient Secant-Like Methods. Journal of Function Spaces 2014, pages 1-10.
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Ioannis K. Argyros & Sanjay K. Khattri. (2013) On an iterative algorithm of Ulm-type for solving equations. Journal of Numerical Analysis and Approximation Theory 42:2, pages 103-114.
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S. Amat, C. Bermúdez, S. Busquier & S. Plaza. (2010) On a third‐order Newton‐type method free of bilinear operators. Numerical Linear Algebra with Applications 17:4, pages 639-653.
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Ioannis K. Argyros & Hongmin Ren. (2008) On a quadratically convergent method using divided differences of order one under the gamma condition. Central European Journal of Mathematics 6:2, pages 262-271.
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Virginia Alarcón, Sergio Amat, Sonia Busquier & David J. López. (2008) A Steffensen's type method in Banach spaces with applications on boundary-value problems. Journal of Computational and Applied Mathematics 216:1, pages 243-250.
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Ioannis K. Argyros. (2007) A Kantorovich-type analysis for a fast iterative method for solving nonlinear equations. Journal of Mathematical Analysis and Applications 332:1, pages 97-108.
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Jinhai Chen & Zuhe Shen. (2007) Convergence analysis of the secant type methods. Applied Mathematics and Computation 188:1, pages 514-524.
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S. Amat & S. Busquier. (2006) A two-step Steffensen's method under modified convergence conditions. Journal of Mathematical Analysis and Applications 324:2, pages 1084-1092.
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Hongmin Ren. (2006) On the local convergence of a deformed Newton's method under Argyros-type condition. Journal of Mathematical Analysis and Applications 321:1, pages 396-404.
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