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

References

  • Dong, C. , 1987. A family of multipoint iterative functions for finding multiple roots of equations , Int. J. Comput. Math. 21 (1987), pp. 363–367.
  • Grau, M. , and Diaz-Barrero, J. L. , 2006. An improvement to Ostrowski root-finding method , Appl. Math. Comput. 173 (2006), pp. 450–456.
  • Halley, E. , 1694. A new, exact and easy method of finding the roots of equations generally and that without any previous reduction , Philos. Trans. R. Soc. Lond. 18 (1694), pp. 136–148.
  • Hansen, E. , and Patrick, M. , 1977. A family of root finding methods , Numer. Math. 27 (1977), pp. 257–269.
  • Homeier, H. H.H. , 2005. On Newton-type methods with cubic convergence , J. Comput. Appl. Math. 176 (2005), pp. 425–432.
  • Jarratt, P. , 1966. Some fourth order multipoint methods for solving equations , Math. Comput. 20 (1966), pp. 434–437.
  • Jarratt, P. , 1966. Multipoint iterative methods for solving certain equations , Comput. J. 8 (1966), pp. 398–400.
  • King, R. F. , 1973. A family of fourth order methods for nonlinear equations , SIAM J. Numer. Amal. 10 (1973), pp. 876–879.
  • Murakami, T. , 1978. Some fifth order multipoint iterative formulae for solving equations , J. Inform. Process 1 (1978), pp. 138–139.
  • Neta, B. , 1983. Numerical Methods for the Solution of Equations . California: Net-A-Sof; 1983.
  • B. Neta and A.N. Johnson, High order nonlinear solver for multiple roots, Computers and Mathematics with Applications, accepted for publication, doi:10.1016/j.camwa.2007.09.001.
  • Ostrowski, A. M. , 1960. Solutions of Equations and System of Equations . New York: Academic Press; 1960.
  • Rall, L. B. , 1966. Convergence of the Newton process to multiple solutions , Numer. Math. 9 (1966), pp. 23–37.
  • Redfern, D. , 1994. The Maple Handbook . New York: Springer-Verlag; 1994.
  • Sharma, J. R. , 2005. A composite third order Newton–Steffensen method for solving nonlinear equations , Appl. Math. Comput. 169 (2005), pp. 242–246.
  • Sharma, J. R. , and Goyal, R. K. , 2006. Fourth-order derivative-free methods for solving non-linear equations , Int. J. Comput. Math. 83 (2006), pp. 101–106.
  • Schröder, E. , 1870. Über unendlich viele Algorithmen zur Auflösung der Gleichungen , Math. Ann. 2 (1870), pp. 317–365.
  • Traub, J. F. , 1964. Iterative Methods for the Solution of Equations . New Jersey: Prentice Hall; 1964.
  • Victory, H. D. , and Neta, B. , 1983. A higher order method for multiple zeros of nonlinear functions , Int. J. Comput. Math. 12 (1983), pp. 329–335.

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.