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International Journal of Computer Mathematics Volume 9, 1981 - Issue 4
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Original Articles

On a family of multipoint methods for non-linear equations

Beny Neta Department of Mathematical Sciences, Northern Illinois University, DeKalb, Illinois, 60115
Pages 353-361 | Received 01 Jul 1981, Published online: 19 Mar 2007

Citations (62)

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Kun Wang & Xinlong Feng. (2011) New predictor–corrector methods of second-order for solving nonlinear equations. International Journal of Computer Mathematics 88:2, pages 296-313.
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J. R. Sharma. (2007) A family of improved Jarratt multipoint methods. International Journal of Computer Mathematics 84:7, pages 1027-1034.
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Beny Neta. (1988) Several new methods for solving equations. International Journal of Computer Mathematics 23:3-4, pages 265-282.
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Articles from other publishers (59)

Quan Zheng & Zhongli Liu. (2023) On general families of multipoint iterations by inverse interpolation and their applications. Journal of Computational and Applied Mathematics 426, pages 115096.
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N. Gupta & J. P. Jaiswal. (2021) Semilocal Convergence of Modified Chebyshev–Halley Method for Nonlinear Operators in Case of Unbounded Third Derivative. Numerical Analysis and Applications 14:1, pages 40-54.
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Ivan Petković & Ðorđe Herceg. (2019) Computers in mathematical research: the study of three-point root-finding methods. Numerical Algorithms 84:3, pages 1179-1198.
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Janak Raj Sharma & Himani Arora. (2019) Efficient Ostrowski-like methods of optimal eighthand sixteenth order convergence and their dynamics. Afrika Matematika 30:5-6, pages 921-941.
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Ali Saleh Alshomrani, Ramandeep Behl & V. Kanwar. (2019) An optimal reconstruction of Chebyshev–Halley type methods for nonlinear equations having multiple zeros. Journal of Computational and Applied Mathematics 354, pages 651-662.
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Ramandeep Behl, S. Amat, Á.A. Magreñán & S.S. Motsa. (2019) An efficient optimal family of sixteenth order methods for nonlinear models. Journal of Computational and Applied Mathematics 354, pages 271-285.
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Min-Young Lee, Young Ik Kim & Beny Neta. (2019) A Generic Family of Optimal Sixteenth-Order Multiple-Root Finders and Their Dynamics Underlying Purely Imaginary Extraneous Fixed Points. Mathematics 7:6, pages 562.
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Mehdi Salimi & Ramandeep Behl. (2019) Sixteenth-Order Optimal Iterative Scheme Based on Inverse Interpolatory Rational Function for Nonlinear Equations. Symmetry 11:5, pages 691.
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Changbum Chun & Beny Neta. (2019) COMPARATIVE STUDY OF METHODS OF VARIOUS ORDERS FOR FINDING SIMPLE ROOTS OF NONLINEAR EQUATIONS. Journal of Applied Analysis & Computation 9:2, pages 400-427.
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Ramandeep Behl, Ali Saleh Alshomrani, Fouad Othman Mallawi & Mohammed Ali A. Mahnashi. (2018) An efficient and optimal higher-order scheme in general way for simple zeros. Journal of Physics: Conference Series 1139, pages 012078.
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Euaggelos E. Zotos, Md Sanam Suraj, Amit Mittal & Rajiv Aggarwal. (2018) Comparing the Geometry of the Basins of Attraction, the Speed and the Efficiency of Several Numerical Methods. International Journal of Applied and Computational Mathematics 4:4.
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Euaggelos E. Zotos. (2018) Comparing the basins of attraction for several methods in the circular Sitnikov problem with spheroid primaries. Astrophysics and Space Science 363:6.
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Euaggelos E. Zotos. (2017) Comparing the fractal basins of attraction in the Hill problem with oblateness and radiation. Astrophysics and Space Science 362:10.
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P. Maroju, Ramandeep Behl & S.S. Motsa. (2017) Some novel and optimal families of King’s method with eighth and sixteenth-order of convergence. Journal of Computational and Applied Mathematics 318, pages 136-148.
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Changbum Chun & Beny Neta. (2016) Comparative study of eighth-order methods for finding simple roots of nonlinear equations. Numerical Algorithms 74:4, pages 1169-1201.
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Gunar Matthies, Mehdi Salimi, Somayeh Sharifi & Juan Luis Varona. (2016) An optimal three-point eighth-order iterative method without memory for solving nonlinear equations with its dynamics. Japan Journal of Industrial and Applied Mathematics 33:3, pages 751-766.
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Ramandeep Behl & S. S. Motsa. (2016) Higher Order Two-Point Efficient Family of Halley Type Methods for Simple Roots. International Journal of Computational Methods 13:04, pages 1641016.
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Somayeh Sharifi, Stefan Siegmund & Mehdi Salimi. (2015) Solving nonlinear equations by a derivative-free form of the King’s family with memory. Calcolo 53:2, pages 201-215.
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Changbum Chun & Beny Neta. (2016) An analysis of a Khattri’s 4th order family of methods. Applied Mathematics and Computation 279, pages 198-207.
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Somayeh Sharifi, Mehdi Salimi, Stefan Siegmund & Taher Lotfi. (2016) A new class of optimal four-point methods with convergence order 16 for solving nonlinear equations. Mathematics and Computers in Simulation 119, pages 69-90.
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Beong In Yun, Miodrag Petković & Jovana Džunić. (2016) On a general transformation of multipoint root-solvers. Journal of Computational and Applied Mathematics 292, pages 136-149.
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Janak Raj Sharma & Himani Arora. (2016) A new family of optimal eighth order methods with dynamics for nonlinear equations. Applied Mathematics and Computation 273, pages 924-933.
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Juan Liang, Xiaowu Li, Zhinan Wu, Mingsheng Zhang, Lin Wang & Feng Pan. (2015) Fifth-Order Iterative Method for Solving Multiple Roots of the Highest Multiplicity of Nonlinear Equation. Algorithms 8:3, pages 656-668.
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Janak Raj Sharma. (2015) Improved Chebyshev–Halley methods with sixth and eighth order convergence. Applied Mathematics and Computation 256, pages 119-124.
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J. R. Sharma & Puneet Gupta. (2015) On Some Highly Efficient Derivative Free Methods With and Without Memory for Solving Nonlinear Equations. International Journal of Computational Methods 12:01, pages 1350093.
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Changbum Chun & Beny Neta. (2015) An analysis of a family of Maheshwari-based optimal eighth order methods. Applied Mathematics and Computation 253, pages 294-307.
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Taher Lotfi, Somayeh Sharifi, Mehdi Salimi & Stefan Siegmund. (2014) A new class of three-point methods with optimal convergence order eight and its dynamics. Numerical Algorithms 68:2, pages 261-288.
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Changbum Chun & Beny Neta. (2014) An analysis of a new family of eighth-order optimal methods. Applied Mathematics and Computation 245, pages 86-107.
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Miquel Grau-Sánchez & Jose L. Diaz-Barrero. (2014) Note on improvements of order and efficiency in some iterative methods for solving nonlinear equations. Applied Mathematics Letters 33, pages 18-22.
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Janak Raj Sharma & Himani Arora. (2014) An efficient family of weighted-Newton methods with optimal eighth order convergence. Applied Mathematics Letters 29, pages 1-6.
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Beny Neta, Changbum Chun & Melvin Scott. (2014) Basins of attraction for optimal eighth order methods to find simple roots of nonlinear equations. Applied Mathematics and Computation 227, pages 567-592.
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Daxin Zhu & Xiaodong Wang. (2013) The Computer Implementations of an Efficient Iterative Algorithm Based on the Inverse Newton Interpolation. The Computer Implementations of an Efficient Iterative Algorithm Based on the Inverse Newton Interpolation.
Changbum Chun & Mi Young Lee. (2013) A new optimal eighth-order family of iterative methods for the solution of nonlinear equations. Applied Mathematics and Computation 223, pages 506-519.
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Alicia Cordero, Jos? L. Hueso, Eulalia Mart?nez & Juan R. Torregrosa. (2013) Generating optimal derivative free iterative methods for nonlinear equations by using polynomial interpolation. Mathematical and Computer Modelling 57:7-8, pages 1950-1956.
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M.S. Petković. (2013) A note on the priority of optimal multipoint methods for solving nonlinear equations. Applied Mathematics and Computation 219:10, pages 5249-5252.
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. 2013. Multipoint Methods. Multipoint Methods 281 291 .
Miodrag S. Petković, Beny Neta, Ljiljana D. Petković & Jovana Džunić. 2013. Multipoint Methods. Multipoint Methods 163 188 .
Miodrag S. Petković, Beny Neta, Ljiljana D. Petković & Jovana Džunić. 2013. Multipoint Methods. Multipoint Methods 109 162 .
Miodrag S. Petković, Beny Neta, Ljiljana D. Petković & Jovana Džunić. 2013. Multipoint Methods. Multipoint Methods 85 108 .
Diyashvir Kreetee Rajiv Babajee & Rajinder Thukral. (2012) On a 4-Point Sixteenth-Order King Family of Iterative Methods for Solving Nonlinear Equations. International Journal of Mathematics and Mathematical Sciences 2012, pages 1-13.
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Alicia Cordero, Mojtaba Fardi, Mehdi Ghasemi & Juan R. Torregrosa. (2012) A Family of Iterative Methods with Accelerated Eighth-Order Convergence. Journal of Applied Mathematics 2012, pages 1-9.
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J.M. McNamee & Victor Y. Pan. (2012) Efficient polynomial root-refiners: A survey and new record efficiency estimates. Computers & Mathematics with Applications 63:1, pages 239-254.
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Melvin Scott, Beny Neta & Changbum Chun. (2011) Basin attractors for various methods. Applied Mathematics and Computation 218:6, pages 2584-2599.
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Miodrag S. Petković, Jovana Džunić & Beny Neta. (2011) Interpolatory multipoint methods with memory for solving nonlinear equations. Applied Mathematics and Computation 218:6, pages 2533-2541.
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Young Hee Geum & Young Ik Kim. (2011) A biparametric family of four-step sixteenth-order root-finding methods with the optimal efficiency index. Applied Mathematics Letters 24:8, pages 1336-1342.
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Xiaowu Li, Chunlai Mu, Jinwen Ma & Linke Hou. (2010) Fifth-order iterative method for finding multiple roots of nonlinear equations. Numerical Algorithms 57:3, pages 389-398.
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Young Hee Geum & Young Ik Kim. (2011) A family of optimal sixteenth-order multipoint methods with a linear fraction plus a trivariate polynomial as the fourth-step weighting function. Computers & Mathematics with Applications 61:11, pages 3278-3287.
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Sanjay Kumar Khattri. (2011) Optimal Eighth Order Iterative Methods. Mathematics in Computer Science 5:2, pages 237-243.
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Sanjay Kumar Khattri & Torgrim Log. (2010) Derivative free algorithm for solving nonlinear equations. Computing 92:2, pages 169-179.
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Young Hee Geum & Young Ik Kim. (2011) A biparametric family of optimally convergent sixteenth-order multipoint methods with their fourth-step weighting function as a sum of a rational and a generic two-variable function. Journal of Computational and Applied Mathematics 235:10, pages 3178-3188.
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SANJAY KUMAR KHATTRI & MUHAMMAD ASLAM NOOR. (2012) SIMPLE YET EFFICIENT ALGORITHM FOR SOLVING NONLINEAR EQUATIONS. International Journal of Modeling, Simulation, and Scientific Computing 01:04, pages 509-522.
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B. Neta & M.S. Petković. (2010) Construction of optimal order nonlinear solvers using inverse interpolation. Applied Mathematics and Computation 217:6, pages 2448-2455.
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Young Hee Geum & Young Ik Kim. (2010) A penta-parametric family of fifteenth-order multipoint methods for nonlinear equations. Applied Mathematics and Computation 217:6, pages 2311-2319.
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M.S. Petkovi?S. Ili?J. D?uni?. (2010) Derivative free two-point methods with and without memory for solving nonlinear equations. Applied Mathematics and Computation 217:5, pages 1887-1895.
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Petkovic MiodragS.S. & Petkovic LjiljanaD.D.. (2010) Families of optimal multipoint methods for solving nonlinear equations: A survey. Applicable Analysis and Discrete Mathematics 4:1, pages 1-22.
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Xiaowu Li, Chunlai Mu, Jinwen Ma & Chan Wang. (2010) Sixteenth-order method for nonlinear equations. Applied Mathematics and Computation 215:10, pages 3754-3758.
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J.R. Sharma & R.K. Guha. (2007) A family of modified Ostrowski methods with accelerated sixth order convergence. Applied Mathematics and Computation 190:1, pages 111-115.
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. 2007. Numerical Methods for Roots of Polynomials, Part I. Numerical Methods for Roots of Polynomials, Part I 131 206 .
A. Griewank. (1985) On Solving Nonlinear Equations with Simple Singularities or Nearly Singular Solutions. SIAM Review 27:4, pages 537-563.
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