New variants of Jarratt's method with sixth-order convergence

Numerical Algorithms

Volumn 52, Issue 4, 2009, Pages 585-603

  Ren, Hongmin ^a   Wu, Qingbiao ^b   Bi, Weihong ^b  

^a Hangzhou Radio & TV University   (China)

^b ZHEJIANG UNIVERSITY   (China)

Author keywords

Iterative methods; Jarratt's method; Nonlinear equations; Order of convergence; Two variable Taylor expansion formula

Indexed keywords

EID: 76149090807     PISSN: 10171398     EISSN: 15729265     Source Type: Journal    
DOI: 10.1007/s11075-009-9302-3     Document Type: Article

References (22)

1. Ortega, J. M., Rheinbolt, W. C.: Iterative Solution of Nonlinear Equations in Servral Variables. Academic, New York (1970).
2. Argyros, I. K.: Convergence and Application of Newton-Type Iterations. Springer, New York (2008).
3. Ostrowski, A. M.: Solution of Equations in Euclidean and Banach Spaces. Academic, New York (1960).
4. Traub, J. F.: Iterative Methods for the Solution of Equations. Prentice-Hall, Englewood Cliffs (1964).
5. Jarratt, P.: Some fourth order multipoint iterative methods for solving equations. Math. Comput. 20(95), 434-437 (1966).
6. King, R. F.: A family of fourth order methods for nonlinear equations. SIAM J. Numer. Anal. 10, 876-879 (1973).
7. Argyros, I. K., Chen, D., Qian, Q.: The Jarratt method in Banach space setting. J. Comput. Appl. Math. 51, 103-106 (1994).
8. Hernandez, M. A., Salanova, M. A.: Relaxing convergence conditions for the Jarratt method. Southwest Journal of Pure and Applied Mathematic 2, 16-19 (1997).
9. Argyros, I. K.: A new convergence theorem for the Jarratt method in Banach space. Comput. Math. Appl. 36, 13-18 (1998).
10. Weerakoon, S., Fernando, T. G. I.: A variant of Newton's method with accelerated third-order convergence. Appl. Math. Lett. 13, 87-93 (2000).
11. Amat, S., Busquier, S., Plaza, S.: Dynamics of the King and Jarratt iterations. Aequ. Math. 69, 212-223 (2005).
12. Grau, M., Díaz-Barrero, J. L.: An improvement to Ostrowski root-finding method. Appl. Math. Comput. 173, 450-456 (2006).
13. Kou, J., Li, Y., Wang, X.: An improvement of the Jarrat method. Appl. Math. Comput. 189, 1816-1821 (2007).
14. Sharma, J. R., Guha, R. K.: A family of modified Ostrowski methods with accelerated sixth-order convergence. Appl. Math. Comput. 190, 111-115 (2007).
15. Chun, C.: Some improvements of Jarratt's method with sixth-order convergence. Appl. Math. Comput. 190, 1432-1437 (2007).
16. Chun, C., Ham, Y.: Some sixth-order variants of Ostrowski root-finding methods. Appl. Math. Comput. 193, 389-394 (2007).
17. Kou, J., Li, Y., Wang, X.: Some variants of Ostrowski's method with seventh-order convergence. J. Comput. Appl. Math. 209, 153-159 (2007).
18. Grau-Sánchez, M.: Improvements of the efficiency of some three-step iterative like-Newton methods. Numer. Math. 107, 131-146 (2007).
19. Bi, W., Ren, H., Wu, Q.: New family of seventh-order methods for nonlinear equations. Appl. Math. Comput. 203, 408-412 (2008).
20. Wang, X., Kou, J., Li, Y.: A variant of Jarratt method with sixth-order convergence. Appl. Math. Comput. 204, 14-19 (2008).
21. Nedzhibov, G. H.: A family of multi-point iterative methods for solving systems of nonlinear equations. J. Comput. Appl. Math. 222, 244-250 (2008).
22. Bi, W., Ren, H., Wu, Q.: Three-step iterative methods with eighth-order convergence for solving nonlinear equations. J. Comput. Appl. Math. 225, 105-112 (2009).