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International Journal of Computer Mathematics Volume 8, 1980 - Issue 1
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Original Articles

A family of one-point iteration formulae for finding roots

D.B. Popovski Departmen of Engineering, Univesity of Bitola, P.O.Box 99, Bitola, 97000, Yugoslavia
Pages 85-88 | Received 01 Mar 1979, Published online: 19 Mar 2007

Citations (23)

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Read on this site (3)

Mehdi Dehghan & Masoud Hajarian. (2010) New iterative method for solving non-linear equations with fourth-order convergence. International Journal of Computer Mathematics 87:4, pages 834-839.
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T. R. Scavo & J. B. Thoo. (1995) On the Geometry of Halley's Method. The American Mathematical Monthly 102:5, pages 417-426.
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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 (20)

Beny Neta. (2023) On a Fifth-Order Method for Multiple Roots of Nonlinear Equations. Symmetry 15:9, pages 1694.
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Beny Neta. (2022) Basins of attraction for family of Popovski’s methods and their extension to multiple roots. Journal of Numerical Analysis and Approximation Theory 51:1, pages 88-102.
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Đ. Herceg & I. Petković. (2022) Computer visualization and dynamic study of new families of root-solvers. Journal of Computational and Applied Mathematics 401, pages 113775.
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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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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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Changbum Chun & Beny Neta. (2018) Comparative study of methods of various orders for finding repeated roots of nonlinear equations. Journal of Computational and Applied Mathematics 340, pages 11-42.
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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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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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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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Beny Neta & Melvin Scott. (2013) On a family of Halley-like methods to find simple roots of nonlinear equations. Applied Mathematics and Computation 219:15, pages 7940-7944.
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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 .
Beny Neta, Melvin Scott & Changbum Chun. (2012) Basin attractors for various methods for multiple roots. Applied Mathematics and Computation 218:9, pages 5043-5066.
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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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J.A. Ezquerro, M.A. Hernández & N. Romero. (2009) Newton-type methods of high order and domains of semilocal and global convergence. Applied Mathematics and Computation 214:1, pages 142-154.
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Changbum Chun & Beny Neta. (2008) Some modification of Newton’s method by the method of undetermined coefficients. Computers & Mathematics with Applications 56:10, pages 2528-2538.
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B. Neta. (2008) New third order nonlinear solvers for multiple roots. Applied Mathematics and Computation 202:1, pages 162-170.
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B. Neta. (2008) On Popovski’s method for nonlinear equations. Applied Mathematics and Computation 201:1-2, pages 710-715.
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Bahman Kalantari, Iraj Kalantari & Rahim Zaare-Nahandi. (1997) A basic family of iteration functions for polynomial root finding and its characterizations. Journal of Computational and Applied Mathematics 80:2, pages 209-226.
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A. Melman. (1997) Classroom Note:Geometry and Convergence of Euler's and Halley's Methods. SIAM Review 39:4, pages 728-735.
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D. B. Popovski. (1982) Sixth order methods for solving equations. ZAMP Zeitschrift f�r angewandte Mathematik und Physik 33:3, pages 434-438.
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