Chebyshev-Halley methods for analytic functions

Journal of Computational and Applied Mathematics

Volumn 216, Issue 2, 2008, Pages 585-599

  Osada, Naoki ^a  

^a TOKYO WOMAN'S CHRISTIAN UNIVERSITY   (Japan)

Author keywords

Analytic function; Chebyshev Halley method; Chebyshev Halley like method; Decreasing ratio; Multiple zero; Simultaneous; Zero finding

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; FUNCTION EVALUATION; POLYNOMIALS;

ANALYTIC FUNCTION;

CHEBYSHEV APPROXIMATION;

EID: 41949096396     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2007.06.020     Document Type: Article

References (29)

1. Amat S., Busquier S., and Plaza S. A construction of attracting periodic orbits for some classical third-order iterative methods. J. Comput. Appl. Math. 189 (2006) 22-33
2. Argyros I.K., Chen D., and Qian Q.S. A convergence analysis for rational methods with a parameter in a Banach space. Pure Math. Appl. 5 (1994) 59-73
3. Bodewig E. Sur la méthods de Laguerre pour l'approximation des racines de certaines équations algébriques et sur la critique d'Hermite. Akad. Wetensh. Proc. (Amsterdam) 49 (1946) 911-921
4. Chen D., Argyros I.K., and Qian Q.S. A local convergence for the super-Halley method in Banach spaces. Appl. Math. Lett. 7 (1994) 49-52
5. E. Durand, Solutions Numériques des Equations Algébriques, Tome I, Masson et Cie, Paris, 1960.
6. Farmer M.R., and Loizou G. An algorithm for the total, or partial, factorization of a polynomial. Math. Proc. Cambridge Philos. Soc. 82 (1977) 427-437
7. Gargantini I. Further applications of circular arithmetic: Schroeder-like algorithms with error bounds for finding zeros of polynomials. SIAM J. Numer. Anal. 15 (1978) 497-510
8. Gutiérrez J.M., and Hernández M.A. A family of Chebyshev-Halley type methods in Banach spaces. Bull. Austral. Math. Soc. 55 (1997) 113-130
9. Halley E. Methodus Nova Accurata & facilis inveniendi Radices Æqùationum quarumcumque genereliter, sine prævia Reductione. Philos. Trans. Roy. Soc. London 18 (1694) 136-148
10. Hansen E., and Patrick M. A family of root finding methods. Numer. Math. 27 (1977) 257-269
11. Hansen E., Patrick M., and Rusnak J. Some modifications of Laguerre's method. BIT 17 (1977) 409-417
12. P. Henrici, Applied and Computational Complex Analysis, vol. I, Wiley, New York, 1974.
13. Hernández Verón M.A. Newton-Raphson's method and convexity. Univ. u Novom Sadu Zb. Rad. Period.-Mat. Fak. Ser. Mat. 22 (1992) 159-166
14. Hernández M.A., and Salanova M.A. A family of Chebyshev-Halley type methods. Internat. J. Comput. Math. 47 (1993) 59-63
15. ISO/IEC 9899:1999, Programming languages- C 〈http://www.iso.org/〉.
16. Kravanja P., Sakurai T., and Van Barel M. On locating clusters of zeros of analytic functions. BIT 39 (1999) 646-682
17. e serié, t. XIX 1880.)
18. Osada N. An optimal root-finding method of order three. J. Comput. Appl. Math. 54 (1994) 131-133
19. Osada N. Asymptotic error constants of cubically convergent zero finding methods. J. Comput. Appl. Math. 196 (2006) 347-357
20. Osada N. A one parameter family of locally quartically convergent zero-finding methods. J. Comput. Appl. Math. 205 (2007) 116-128
21. Ostrowski A.M. Solution of Equations in Banach Spaces (1973), Academic Press, New York
22. Petković L.D., Petković M.S., and Živković D. Hansen-Patrick's family is of Laguerre's type. Novi Sad J. Math. 33 (2003) 109-115
23. Petković M.S., and Rančić L. A new fourth-order family of simultaneous methods for finding polynomial zeros. Appl. Math. Comput. 164 (2005) 227-248
24. Petković M.S., Sakurai T., and Rančić L. Family of simultaneous methods of Hansen-Patrick's type. Appl. Numer. Math. 50 (2004) 489-510
25. Petković M.S., Stefanović L.V., and Marjanović Z.M. On the R-order of some accelerated methods for the simultaneous finding of polynomial zeros. Computing 49 (1993) 349-361
26. Schröder E. Über unendlich viele Algorithmen zur Auflösung der Gleichungen. Math. Ann. 2 (1870) 317-365
27. R.M. Stallman and the GCC Developer Community, Using the GNU Compiler Collection 〈http://www.gcc.gnu.org/onlinedocs/gcc-4.1.2/gcc.pdf〉.
28. Traub J.F. Iterative Methods for the Solution of Equations. second ed. (1982), Chelsea, New York
29. W. Werner, Some improvement of classical methods for the solution of nonlinear equations, in: Numerical Solution of Nonlinear Equations, Lecture Notes in Mathematics, vol. 878, 1981, pp. 426-440.