Advanced search
Publication Cover
International Journal of Computer Mathematics Volume 87, 2010 - Issue 5
Submit an article Journal homepage
128
Views
58
CrossRef citations to date
0
Altmetric
Section B

Extension of Murakami's high-order non-linear solver to multiple roots

B. Neta Department of Applied Mathematics, Naval Postgraduate School , Monterey, CA, USA
Pages 1023-1031 | Received 05 Sep 2007, Accepted 06 Jun 2008, Published online: 10 May 2010

Citations (58)

Keep up to date with the latest research on this topic with citation updates for this article.

Subscribe to citation updates

Read on this site (1)

Gyurhan H. Nedzhibov. (2013) Iterative methods for simultaneous computing arbitrary number of multiple zeros of nonlinear equations. International Journal of Computer Mathematics 90:5, pages 994-1007.
Read now

Articles from other publishers (57)

Young Hee Geum. (2023) On Constructing a Family of Sixth-Order Methods for Multiple Roots. Fractal and Fractional 7:12, pages 878.
Crossref
Rongfei Lin, Hongmin Ren, Qingbiao Wu, Yasir Khan & Juelian Hu. (2021) Convergence Analysis of the Modified Chebyshev’s Method for Finding Multiple Roots. Vietnam Journal of Mathematics 50:1, pages 59-68.
Crossref
J. R. Sharma & H. Arora. (2021) A Family of Fifth-Order Iterative Methods for Finding Multiple Roots of Nonlinear Equations. Numerical Analysis and Applications 14:2, pages 186-199.
Crossref
Deepak Kumar, Sunil Kumar, Janak Raj Sharma & Matteo d’Amore. (2020) Generating Optimal Eighth Order Methods for Computing Multiple Roots. Symmetry 12:12, pages 1947.
Crossref
Munish Kansal, Alicia Cordero, Juan R. Torregrosa & Sonia Bhalla. (2020) A stable class of modified Newton-like methods for multiple roots and their dynamics. International Journal of Nonlinear Sciences and Numerical Simulation 21:6, pages 603-621.
Crossref
Fiza Zafar, Alicia Cordero & Juan R. Torregrosa. (2018) A family of optimal fourth‐order methods for multiple roots of nonlinear equations. Mathematical Methods in the Applied Sciences 43:14, pages 7869-7884.
Crossref
Ramandeep Behl, Ioannis K. Argyros, Michael Argyros, Mehdi Salimi & Arwa Jeza Alsolami. (2020) An Iteration Function Having Optimal Eighth-Order of Convergence for Multiple Roots and Local Convergence. Mathematics 8:9, pages 1419.
Crossref
Ramandeep Behl, Munish Kansal & Mehdi Salimi. (2020) Modified King’s Family for Multiple Zeros of Scalar Nonlinear Functions. Mathematics 8:5, pages 827.
Crossref
Fiza Zafar, Alicia Cordero, Moin-Ud-Din Junjua & Juan R. Torregrosa. (2020) Optimal eighth-order iterative methods for approximating multiple zeros of nonlinear functions. Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas 114:2.
Crossref
Ramandeep Behl, Fiza Zafar, Moin‐ud‐Din Junjua & Ali Saleh Alshomrani. (2020) A new two‐point scheme for multiple roots of nonlinear equations. Mathematical Methods in the Applied Sciences 43:5, pages 2421-2443.
Crossref
Rajni Sharma & Ashu Bahl. (2019) On developing a novel sixth order transformation method for multiple roots and its basins of attraction. SeMA Journal 76:4, pages 595-613.
Crossref
Ramandeep Behl & Waleed M. Al-Hamdan. (2019) A 4th-Order Optimal Extension of Ostrowski’s Method for Multiple Zeros of Univariate Nonlinear Functions. Mathematics 7:9, pages 803.
Crossref
Saima Akram, Fiza Zafar & Nusrat Yasmin. (2019) An Optimal Eighth-Order Family of Iterative Methods for Multiple Roots. Mathematics 7:8, pages 672.
Crossref
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.
Crossref
Fiza Zafar, Alicia Cordero & Juan R. Torregrosa. (2018) Stability analysis of a family of optimal fourth-order methods for multiple roots. Numerical Algorithms 81:3, pages 947-981.
Crossref
R. A. Alharbey, Munish Kansal, Ramandeep Behl & J. A. Tenreiro Machado. (2019) Efficient Three-Step Class of Eighth-Order Multiple Root Solvers and Their Dynamics. Symmetry 11:7, pages 837.
Crossref
Ramandeep Behl, Fiza Zafar, Ali Saleh Alshormani, Moin-Ud-Din Junjua & Nusrat Yasmin. (2019) An Optimal Eighth-Order Scheme for Multiple Zeros of Univariate Functions. International Journal of Computational Methods 16:04, pages 1843002.
Crossref
Munish Kansal, Ramandeep Behl, Mohammed Ali A. Mahnashi & Fouad Othman Mallawi. (2019) Modified Optimal Class of Newton-Like Fourth-Order Methods for Multiple Roots. Symmetry 11:4, pages 526.
Crossref
Janak Raj Sharma, Deepak Kumar & Ioannis K. Argyros. (2019) An Efficient Class of Traub-Steffensen-Like Seventh Order Multiple-Root Solvers with Applications. Symmetry 11:4, pages 518.
Crossref
Ramandeep Behl, Eulalia Martínez, Fabricio Cevallos & Diego Alarcón. (2019) A Higher Order Chebyshev-Halley-Type Family of Iterative Methods for Multiple Roots. Mathematics 7:4, pages 339.
Crossref
Ramandeep Behl, Eulalia Martínez, Fabricio Cevallos & Ali S. Alshomrani. (2019) Local Convergence Balls for Nonlinear Problems with Multiplicity and Their Extension to Eighth-Order Convergence. Mathematical Problems in Engineering 2019, pages 1-17.
Crossref
Ramandeep Behl, Eulalia Martínez, Fabricio Cevallos & Ali Saleh Alshomrani. 2019. Finite Difference Methods. Theory and Applications. Finite Difference Methods. Theory and Applications 153 158 .
Fiza Zafar, Alicia Cordero & Juan Torregrosa. (2018) An Efficient Family of Optimal Eighth-Order Multiple Root Finders. Mathematics 6:12, pages 310.
Crossref
Fiza Zafar, Alicia Cordero, Sana Sultana & Juan R. Torregrosa. (2018) Optimal iterative methods for finding multiple roots of nonlinear equations using weight functions and dynamics. Journal of Computational and Applied Mathematics 342, pages 352-374.
Crossref
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.
Crossref
P. Maroju, Á. A. Magreñán, S. S. Motsa & Í. Sarría. (2018) Second derivative free sixth order continuation method for solving nonlinear equations with applications. Journal of Mathematical Chemistry 56:7, pages 2099-2116.
Crossref
Ramandeep Behl, Ali Saleh Alshomrani & S. S. Motsa. (2018) An optimal scheme for multiple roots of nonlinear equations with eighth-order convergence. Journal of Mathematical Chemistry 56:7, pages 2069-2084.
Crossref
Young Hee Geum, Young Ik Kim & Beny Neta. (2018) Constructing a family of optimal eighth-order modified Newton-type multiple-zero finders along with the dynamics behind their purely imaginary extraneous fixed points. Journal of Computational and Applied Mathematics 333, pages 131-156.
Crossref
Ramandeep Behl, Alicia Cordero, Sandile S. Motsa & Juan R. Torregrosa. (2017) An eighth-order family of optimal multiple root finders and its dynamics. Numerical Algorithms 77:4, pages 1249-1272.
Crossref
Young Hee Geum, Young Ik Kim & Beny Neta. (2017) A family of optimal quartic-order multiple-zero finders with a weight function of the principal th root of a derivative-to-derivative ratio and their basins of attraction . Mathematics and Computers in Simulation 136, pages 1-21.
Crossref
Young Hee Geum, Young Ik Kim & Beny Neta. (2016) A sixth-order family of three-point modified Newton-like multiple-root finders and the dynamics behind their extraneous fixed points. Applied Mathematics and Computation 283, pages 120-140.
Crossref
Jai Jaiswal. (2016) An Optimal Order Method for Multiple Roots in Case of Unknown Multiplicity. Algorithms 9:1, pages 10.
Crossref
Rajni Sharma & Ashu Bahl. (2015) A sixth order transformation method for finding multiple roots of nonlinear equations and basin attractors for various methods. Applied Mathematics and Computation 269, pages 105-117.
Crossref
Changbum Chun & Beny Neta. (2015) Comparing the basins of attraction for Kanwar–Bhatia–Kansal family to the best fourth order method. Applied Mathematics and Computation 266, pages 277-292.
Crossref
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.
Crossref
Changbum Chun & Beny Neta. (2015) Basins of attraction for Zhou–Chen–Song fourth order family of methods for multiple roots. Mathematics and Computers in Simulation 109, pages 74-91.
Crossref
José L. Hueso, Eulalia Martínez & Carles Teruel. (2014) Determination of multiple roots of nonlinear equations and applications. Journal of Mathematical Chemistry 53:3, pages 880-892.
Crossref
Beny Neta & Changbum Chun. (2014) Basins of attraction for several optimal fourth order methods for multiple roots. Mathematics and Computers in Simulation 103, pages 39-59.
Crossref
D. Sbibih, A. Serghini, A. Tijini & A. Zidna. (2014) A general family of third order method for finding multiple roots. Applied Mathematics and Computation 233, pages 338-350.
Crossref
Xiaojian Zhou, Xin Chen & Yongzhong Song. (2013) On the convergence radius of the modified Newton method for multiple roots under the center–Hölder condition. Numerical Algorithms 65:2, pages 221-232.
Crossref
R. F. Lin, H. M. Ren, Z. Šmarda, Q. B. Wu, Y. Khan & J. L. Hu. (2014) New Families of Third-Order Iterative Methods for Finding Multiple Roots. Journal of Applied Mathematics 2014, pages 1-9.
Crossref
Young Ik Kim & Young Hee Geum. (2014) A New Biparametric Family of Two-Point Optimal Fourth-Order Multiple-Root Finders. Journal of Applied Mathematics 2014, pages 1-7.
Crossref
Beny Neta, Changbum Chun & Melvin Scott. (2013) On the development of iterative methods for multiple roots. Applied Mathematics and Computation 224, pages 358-361.
Crossref
Young Ik Kim. (2013) ON A GENERAL CLASS OF OPTIMAL FOURTH-ORDER MULTIPLE-ROOT FINDERS. Journal of the Chungcheong Mathematical Society 26:3, pages 657-669.
Crossref
Young Ik Kim & Young Hee Geum. (2013) A Two-Parameter Family of Fourth-Order Iterative Methods with Optimal Convergence for Multiple Zeros. Journal of Applied Mathematics 2013, pages 1-7.
Crossref
. 2013. Multipoint Methods. Multipoint Methods 281 291 .
Miodrag S. Petković, Beny Neta, Ljiljana D. Petković & Jovana Džunić. 2013. Multipoint Methods. Multipoint Methods 27 83 .
Janak Raj Sharma & Rajni Sharma. (2012) Modified Chebyshev-Halley type method and its variants for computing multiple roots. Numerical Algorithms 61:4, pages 567-578.
Crossref
Beong In Yun. (2012) Iterative methods for solving nonlinear equations with finitely many roots in an interval. Journal of Computational and Applied Mathematics 236:13, pages 3308-3318.
Crossref
Sanjeev Kumar, V. Kanwar & Sukhjit Singh. (2012) On some modified families of multipoint iterative methods for multiple roots of nonlinear equations. Applied Mathematics and Computation 218:14, pages 7382-7394.
Crossref
Beny Neta, Melvin Scott & Changbum Chun. (2012) Basin attractors for various methods for multiple roots. Applied Mathematics and Computation 218:9, pages 5043-5066.
Crossref
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.
Crossref
Xiaojian Zhou, Xin Chen & Yongzhong Song. (2011) Constructing higher-order methods for obtaining the multiple roots of nonlinear equations. Journal of Computational and Applied Mathematics 235:14, pages 4199-4206.
Crossref
Hongmin Ren & Ioannis K. Argyros. (2010) Convergence radius of the modified Newton method for multiple zeros under Hölder continuous derivative. Applied Mathematics and Computation 217:2, pages 612-621.
Crossref
S.G. Li, L.Z. Cheng & B. Neta. (2010) Some fourth-order nonlinear solvers with closed formulae for multiple roots. Computers & Mathematics with Applications 59:1, pages 126-135.
Crossref
Li Shengguo, Liao Xiangke & Cheng Lizhi. (2009) A new fourth-order iterative method for finding multiple roots of nonlinear equations. Applied Mathematics and Computation 215:3, pages 1288-1292.
Crossref
Changbum Chun & Beny Neta. (2009) A third-order modification of Newton’s method for multiple roots. Applied Mathematics and Computation 211:2, pages 474-479.
Crossref

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Order Reprints Request Corporate Permissions

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

Request Academic Permissions

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.