Two-point methods

Miodrag S. Petković, Beny Neta, Ljiljana D. Petković, Jovana Džunić

Type: Book-Chapter

Publication Date: 2012-12-14

Citations: 82

DOI: https://doi.org/10.1016/b978-0-12-397013-8.00002-9

View

Locations

Elsevier eBooks - View

Similar Works

Action	Title	Year	Authors
+	Ideal Point Methods	2024
+	Cavallo Point Methods	2010
+	Fixed Point Methods	2012
+	Three-point optimal methods	2012	Miodrag S. Petković Beny Neta Ljiljana D. Petković Jovana Džunić
+	Three-point non-optimal methods	2012	Miodrag S. Petković Beny Neta Ljiljana D. Petković Jovana Džunić
+	Two-point functions	2012	S. A. Fulling
+	Two-Point Newton-Like Methods	2005
+	Extremal Point Methods	2024	Edward B. Saff Вилмос Тотик
+	First-Order Methods	2017	Zhu Han Mingyi Hong Wang Dan
+	Iterative Methods	2018	R. C. Aster Brian Borchers C. H. Thurber
+	Iterative Methods	1966	Lothar Collatz
+	Iterative Methods	2013	Robert M. Corless Nicolas Fillion
+	Fourier methods	1997	Michael J. Chapman D.P. Goodall N. C. Steele
+	Fourier methods	1950	S. Charp
+	Multipoint methods with memory	2012	Miodrag S. Petković Beny Neta Ljiljana D. Petković Jovana Džunić
+	three-point problem method	2014
+	High-order methods	1994	J. M. Sanz‐Serna M. P. Calvo
+	Derivative-Free Methods	2023	Jeffrey Paul Wheeler
+	SECOND-DEGREE METHODS	1971	David M. Young
+	Two-step Newton methods	2018	Á. Alberto Magreñàn Ioannis K. Argyros

Cited by (99)

Action	Title	Year	Authors
+ PDF Chat	Root-multiplicity and root iterative refinement	2023	Jovana Džunić
+ PDF Chat	Choosing the Optimal Multi-Point Iterative Method for the Colebrook Flow Friction Equation	2018	Pavel Praks Dejan Brkić
+	Computers in mathematical research: the study of three-point root-finding methods	2019	Ivan Petković Dejana Herceg
+ PDF Chat	Semilocal Convergence of the Extension of Chun’s Method	2021	Alicia Cordero Javier G. Maimó Eulalia Martı́nez Juan R. Torregrosa María P. Vassileva
+	On the guaranteed convergence of new two-point root-finding methods for polynomial zeros	2013	Miodrag S. Petković L. Rančić
+ PDF Chat	An Optimal Derivative Free Family of Chebyshev–Halley’s Method for Multiple Zeros	2021	Ramandeep Behl Sonia Bhalla Á. Alberto Magreñán Alejandro Moysi
+ PDF Chat	A new fourth-order family for solving nonlinear problems and its dynamics	2014	Alicia Cordero Yufeng Li Á. Alberto Magreñán Juan R. Torregrosa
+ PDF Chat	Local Convergence of Traub’s Method and Its Extensions	2023	M. Saeed Krishnendu Remesh Santhosh George P. Jidesh Ioannis K. Argyros
+ PDF Chat	Derivative-Free King’s Scheme for Multiple Zeros of Nonlinear Functions	2021	Ramandeep Behl Sonia Bhalla Eulalia Martı́nez Majed Aali Alsulami
+ PDF Chat	Extension of King’s Iterative Scheme by Means of Memory for Nonlinear Equations	2023	Saima Akram Maira Khalid Moin‐ud‐Din Junjua Shazia Altaf Sunil Kumar
+ PDF Chat	A stable class of modified Newton-like methods for multiple roots and their dynamics	2020	Munish Kansal Alicia Cordero Juan R. Torregrosa Sonia Bhalla
+ PDF Chat	New modification of Maheshwari’s method with optimal eighth order convergence for solving nonlinear equations	2016	Somayeh Sharifi Массимилиано Феррара Mehdi Salimi Stefan Siegmund
+	Stability of different families of iterative methods with memory	2018	Francisco I. Chicharro Alicia Cordero Juan R. Torregrosa
+	Extended iterative schemes based on decomposition for nonlinear models	2021	Ioannis K. Argyros Debasis Sharma Christopher I. Argyros Sanjaya Kumar Parhi Shanta Kumari Sunanda
+	Dynamical analysis of an iterative method with memory on a family of third-degree polynomials	2022	B. Campos Alicia Cordero Juan R. Torregrosa P. Vindel
+	Some new weighted eighth-order variants of Steffensen-King’s type family for solving nonlinear equations and its dynamics	2016	V. Kanwar Raj Bala Munish Kansal
+ PDF Chat	Two Families of Multipoint Root-Solvers Using Inverse Interpolation with Memory	2023	Zhongli Liu Quan Zheng
+	Two general higher-order derivative free iterative techniques having optimal convergence order	2019	Ramandeep Behl Ali Saleh Alshomrani Á. Alberto Magreñán
+ PDF Chat	A simple algorithm for high order Newton iteration formulae and some new variants	2019	Mustafa Türkyılmazoğlu
+	Improved Chebyshev–Halley family of methods with seventh and eighth order of convergence for simple roots	2017	Ramandeep Behl Ioannis K. Argyros S. S. Motsa
+ PDF Chat	A family of Newton-type methods with seventh and eighth-order of convergence for solving systems of nonlinear equations	2023	Т. Жанлав R. Mijiddorj Khuder Otgondorj
+	On the Convergence, Dynamics and Applications of a New Class of Nonlinear System Solvers	2020	Ioannis K. Argyros Debasis Sharma Sanjaya Kumar Parhi Shanta Kumari Sunanda
+ PDF Chat	Achieving Optimal Order in a Novel Family of Numerical Methods: Insights from Convergence and Dynamical Analysis Results	2024	Marlon Moscoso-Martínez Francisco I. Chicharro Alicia Cordero Juan R. Torregrosa Gabriela Ureña-Callay
+ PDF Chat	On an iterative method without inverses of derivatives for solving equations	2020	Santhosh George Ioannis K. Argyros
+ PDF Chat	New Iterative Methods for Solving Nonlinear Problems with One and Several Unknowns	2018	Ramandeep Behl Alicia Cordero Juan R. Torregrosa Ali Saleh Alshomrani
+ PDF Chat	Convergence and Dynamics of a Higher-Order Method	2020	Alejandro Moysi Ioannis K. Argyros Samundra Regmi Daniel González Á. Alberto Magreñán Juan Antonio Sicilia Montalvo
+	Ball convergence theorems and the convergence planes of an iterative method for nonlinear equations	2015	Á. Alberto Magreñán Ioannis K. Argyros
+ PDF Chat	Modified King’s Family for Multiple Zeros of Scalar Nonlinear Functions	2020	Ramandeep Behl Munish Kansal Mehdi Salimi
+ PDF Chat	Convergence and Stability of a Parametric Class of Iterative Schemes for Solving Nonlinear Systems	2021	Alicia Cordero Eva G. Villalba Juan R. Torregrosa Paula Triguero‐Navarro
+ PDF Chat	Solving Nonlinear Transcendental Equations by Iterative Methods with Conformable Derivatives: A General Approach	2023	Giro Candelario Alicia Cordero Juan R. Torregrosa María P. Vassileva
+ PDF Chat	Sixteenth-Order Optimal Iterative Scheme Based on Inverse Interpolatory Rational Function for Nonlinear Equations	2019	Mehdi Salimi Ramandeep Behl
+ PDF Chat	A Generic Family of Optimal Sixteenth-Order Multiple-Root Finders and Their Dynamics Underlying Purely Imaginary Extraneous Fixed Points	2019	Min Young Lee Young Ik Kim Beny Neta
+ PDF Chat	A New Class of Iterative Processes for Solving Nonlinear Systems by Using One Divided Differences Operator	2019	Alicia Cordero Cristina Jordán Esther Sanabria Codesal Juan R. Torregrosa
+ PDF Chat	Optimal Derivative-Free Root Finding Methods Based on Inverse Interpolation	2019	Moin‐ud‐Din Junjua Fiza Zafar Nusrat Yasmin
+ PDF Chat	An Optimal Derivative-Free Ostrowski’s Scheme for Multiple Roots of Nonlinear Equations	2020	Ramandeep Behl Samaher Khalaf Alharbi Fouad Mallawi Mehdi Salimi
+ PDF Chat	Using Matrix Eigenvalues to Construct an Iterative Method with the Highest Possible Efficiency Index Two	2022	Malik Zaka Ullah Vali Torkashvand Stanford Shateyi Mir Asma
+	A third-order iterative algorithm for inversion of cumulative central beta distribution	2023	Dhivya Prabhu K Sanjeev Singh Antony Vijesh
+	A stable class of improved second-derivative free Chebyshev-Halley type methods with optimal eighth order convergence	2015	Alicia Cordero Munish Kansal V. Kanwar Juan R. Torregrosa
+ PDF Chat	An efficient two-parametric family with memory for nonlinear equations	2014	Alicia Cordero Taher Lotfi Parisa Bakhtiari Juan R. Torregrosa
+ PDF Chat	Two-Point Iterative Methods for Solving Quadratic Equations and its Applications	2018	Kalyanasundaram Madhu

Citing (71)

Action	Title	Year	Authors
+	A family of multiopoint iterative functions for finding multiple roots of equations	1987	Chen Dong
+	Review of some iterative root-finding methods from a dynamical point of view	2004	Sergio Amat Sonia Busquier Sergio Plaza
+	On a class of quadratically convergent iteration formulae	2004	Mamta V. Kanwar V. K. Kukreja Sukhjit Singh
+	Modified Jarratt method for computing multiple roots	2010	Janak Raj Sharma Rajni Sharma
+	On Newton-type methods with cubic convergence	2004	Herbert H. H. Homeier
+ PDF Chat	Optimal Order of One-Point and Multipoint Iteration	1974	H. T. Kung J. F. Traub
+	Solution of Equations and Systems of Equations	1967	E. I. Alexander Ostrowski
+ PDF Chat	Extension of Murakami's high-order non-linear solver to multiple roots	2008	Beny Neta
+	A modified Newton method for rootfinding with cubic convergence	2003	Herbert H. H. Homeier
+	A fourth order iterative method for solving nonlinear equations	2009	Amit Kumar Maheshwari
+	A secant method for multiple roots	1977	Richard F. King
+	Some fourth-order nonlinear solvers with closed formulae for multiple roots	2009	Siwei Li Lizhi Cheng Beny Neta
+	Some variants of Chebyshev–Halley methods free from second derivative	2007	Changbum Chun
+	New higher order methods for solving nonlinear equations with multiple roots	2010	Beong In Yun
+	New high-order convergence iteration methods without employing derivatives for solving nonlinear equations	2001	Xinyuan Wu Fu Dongsheng
+ PDF Chat	Families of optimal multipoint methods for solving nonlinear equations: A survey	2010	Miodrag S. Petković Ljiljana D. Petković
+ PDF Chat	Some fourth order multipoint iterative methods for solving equations	1966	P. Jarratt
+ PDF Chat	A class of Steffensen type methods with optimal order of convergence	2011	Alicia Cordero Juan R. Torregrosa
+	A higher order method for multiple zeros of nonlinear functions	1983	H. D. Victory Beny Neta
+	Fourth-order derivative-free methods for solving non-linear equations	2006	Janak Raj Sharma Rita Goyal
+	An optimal multiple root-finding method of order three	1994	Naoki Osada
+	High-order nonlinear solver for multiple roots	2007	Beny Neta Anthony N. Johnson
+	An improved method for finding multiple roots and it’s multiplicity of nonlinear equations in	2008	P. K. Parida Divyansh Gupta
+	A new fourth-order iterative method for finding multiple roots of nonlinear equations	2009	Shengguo Li Xiangke Liao Cheng Li-zhi
+	Fourth-order iterative methods free from second derivative	2006	Jisheng Kou Yitian Li Xiuhua Wang
+	A family of root finding methods	1976	Eldon Hansen Merrell L. Patrick
+	Some fourth-order iterative methods for solving nonlinear equations	2007	Changbum Chun
+	A family of three-point methods of optimal order for solving nonlinear equations	2009	R. Thukral Miodrag S. Petković
+	Some new variants of Newton's method	2004	Ahmet Yaşar Özban
+	On Newton-type methods for multiple roots with cubic convergence	2009	Herbert H. H. Homeier
+	Constructing higher-order methods for obtaining the multiple roots of nonlinear equations	2011	Xiaojian Zhou Xin Chen Yongzhong Song
+	Derivative free two-point methods with and without memory for solving nonlinear equations	2010	Miodrag S. Petković Sonja Ilić Jovana Džunić
+	A one parameter square root family of two-step root-finders	2006	Miodrag S. Petković Ljiljana D. Petković
+	Iterative methods based on the signum function approach for solving nonlinear equations	2009	Beong In Yun Miodrag S. Petković
+	Some variants of King’s fourth-order family of methods for nonlinear equations	2007	Changbum Chun
+	Several New Third-Order Iterative Methods for Solving Nonlinear Equations	2008	Changbum Chun Yong‐Il Kim
+	Some variant of Newton’s method with third-order convergence	2003	M. Frontini E. Sormani
+ PDF Chat	New third order nonlinear solvers for multiple roots	2008	Beny Neta
+	New families of nonlinear third-order solvers for finding multiple roots	2008	Changbum Chun Hwa ju Bae Beny Neta
+	A family of fourth-order methods for solving non-linear equations	2006	Jisheng Kou Yitian Li Xiuhua Wang