International E-publication: Publish Projects, Dissertation, Theses, Books, Souvenir, Conference Proceeding with ISBN.  International E-Bulletin: Information/News regarding: Academics and Research

A family of modified King's methods with seventh order convergence

Author Affiliations

  • 1Department of Applied Sciences, D.A.V. Institute of Engineering and Technology, Kabirnagar, Jalandhar, INDIA

Res. J. Mathematical & Statistical Sci., Volume 1, Issue (11), Pages 1-6, December,12 (2013)


Based on King's fourth order methods, we derive a family of seventh order methods for the solution of non linear equations. In terms of computational cost the family requires three evaluations of the function and one evaluation of first derivative. The proposed family increases the order of King's fourth order methods and efficiency index from 1.587 to 1.682. The methods are compared with closest competitors in a series of numerical examples and theoretical order of convergence is verified.


  1. Ortega J.M. and Rheinboldt W.C., Iterative Solution of Nonlinear Equations in Several Variables, Academic Press, NewYork, (1970)
  2. Chapra S.C. and Canale R.P., Numerical Methods for Engineers, McGraw-Hill Book Company, New York, (1988)
  3. Traub J.F., Iterative Methods for the Solution of Equations, Prentice-Hall, Englewood Cliffs, NJ, (1964)
  4. King R.F., A family of fourth order methods for nonlinear equations, SIAM J. Numer. Anal., 10, 876-879 (1973)
  5. Ostrowski A.M., Solution of Equations in Euclidean and Banach Spaces, Academic Press, New York, (1960)
  6. Grau M. and Barrero J.L., An improvement to Ostrowski root-finding method, Appl. Math. Comput., 173, 450-456 (2006)
  7. Sharma J.R. and Guha R.K., A family of modified Ostrowski methods with accelerated sixth-order convergence, Appl.Math. Comput, 190, 111-115 (2007)
  8. Chun C.B. and Ham Y.M., Some sixth-order variants of Ostrowski root-finding methods, Appl. Math. Comput., 193, 389-394 (2007)
  9. Kou J. and Biw et al., Li Y. and Wang X., Some variants of Ostrowskis method with seventh-order convergence, J.Comput. Appl. Math., 209, 153-159 (2007)
  10. Bi W., Ren H. and Wu Q., New family of seventh-order methods for nonlinear equations, Appl. Math. Comput. 203, 408412 (2008)
  11. Gautschi W., Numerical Analysis: An Introduction, Birkhuser, Boston, MA, (1997)