A new optimal eighth-order family of multiple root finders

키워드

참고문헌 (25)

1. R. Behl, "An optimal scheme for multiple roots of nonlinear equations with eighth-order convergence", J. Math. Chem, 56(7), pp.2069~2084 (2018)[DOI]
2. R. Behl, "An Iteration Function Having Optimal Eighth-Order of Convergence for Multiple Roots and Local Convergence", Mathematics, 8, pp.1419~ (2020)
3. R. Behl, "An eighth-order family of optimal multiple root finders and its dynamics", Numer. Algorithms, 77(4), pp.1249~1272 (2018)[DOI]
4. R. Behl, "An optimal eighth-order scheme for multiple zeros of univariate functions", Int. J. Comput. Methods, 16(4), pp.1843002~ (2019)[DOI]
5. P. Blanchard, "Complex analytic dynamics on the Riemann sphere", Bull. Amer. Math. Soc. (N.S.), 11(1), pp.85~141 (1984)[DOI]
6. C. Chun, "Basins of attraction for Zhou-Chen-Song fourth order family of methods for multiple roots", Math. Comput. Simulation, 109, pp.74~91 (2015)[DOI]
7. Y. H. Geum, "Constructing a family of optimal eighth-order modified Newton-type multiple-zero finders along with the dynamics behind their purely imaginary extraneous fixed points", J. Comput. Appl. Math, 333, pp.131~156 (2018)[DOI]
8. D. Kumar, "Generating optimal eighth order methods for computing multiple roots", Symmetry, 12, pp.1947~ (2020)
9. H. T. Kung, "Optimal order of one-point and multipoint iteration", J. Assoc. Comput. Mach, 21, pp.643~651 (1974)[DOI]
10. M. -Y. Lee, "On the dynamics of a triparametric family of optimal fourth-order multiple-zero finders with a weight function of the principal mth root of a function-to function ratio", Appl. Math. Comput, 315, pp.564~590 (2017)[DOI]
11. B. Liu, "A new family of fourth-order methods for multiple roots of nonlinear equations", Nonlinear Anal. Model. Control, 18(2), pp.143~152 (2013)
12. B. Neta, "Basins of attraction for several optimal fourth order methods for multiple roots", Math. Comput. Simulation, 103, pp.39~59 (2014)[DOI]
13. M. S. Petković, "Construction and efficiency of multipoint root-ratio methods for finding multiple zeros", J. Comput. Appl. Math, 351, pp.54~65 (2019)[DOI]
14. L. B. Rall, "Convergence of the Newton process to multiple solutions", Numer. Math, 9, pp.23~37 (1966)[DOI]
15. E. Schröder, "Ueber unendlich viele Algorithmen zur Auflösung der Gleichungen", Math. Ann, 2(2), pp.317~365 (1870)[DOI]
16. M. Scott, "Basin attractors for various methods", Appl. Math. Comput, 218(6), pp.2584~2599 (2011)[DOI]
17. J. R. Sharma, "An excellent numerical technique for multiple roots", Math. Comput. Simulation, 182, pp.316~324 (2021)[DOI]
18. B. Stewart, "Attractor basins of various root-finding methods", M.S, pp.2001
19. J. L. Varona, "Graphic and numerical comparison between iterative methods", Math. In-telligencer, 24(1), pp.37~46 (2002)[DOI]
20. E. R. Vrscay, "Extraneous fixed points, basin boundaries and chaotic dynamics for Schröder and König rational iteration functions", Numer. Math, 52(1), pp.1~16 (1988)[DOI]
21. S. Weerakoon, "A variant of Newton’s method with accelerated third-order convergence", Appl. Math. Lett, 13(8), pp.87~93 (2000)[DOI]
22. F. Zafar, "Optimal eighth-order iterative methods for approximating multiple zeros of nonlinear functions", Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM, 114(2), pp.17~ (2020)[DOI]
23. F. Zafar, "Optimal iterative methods for finding multiple roots of nonlinear equations using free parameters", J. Math. Chem, 56(7), pp.1884~1901 (2018)[DOI]
24. F. Zafar, "Optimal iterative methods for finding multiple roots of nonlinear equations using weight functions and dynamics", J. Comput. Appl. Math, 342, pp.352~374 (2018)[DOI]
25. X. Zhou, "Families of third and fourth order methods for multiple roots of nonlinear equations", Appl. Math. Comput, 219(11), pp.6030~6038 (2013)[DOI]

관련 논문AI추천