Seventh-order derivative-free iterative method for solving nonlinear systems (original) (raw)

Access this article

Log in via an institution

Subscribe and save

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  1. Ortega, J.M., Rheinbolt, W.C.: Iterative Solution of Nonlinear Equations in SeveralVariables. Academic Press, New York (1970)
    Google Scholar
  2. Traub, J.F.: Iterative Methods for the Solution of Equations. Prentice-Hall, New Jersey (1964)
    MATH Google Scholar
  3. Dembo, R.S., Eisenstat, S.C., Steihaug, T.: Inexact Newton methods. SIAM. J. Numer. Anal 19, 400–408 (1982)
    Article MATH MathSciNet Google Scholar
  4. Broyden, C.G.: A class of methods for solving nonlinear simultaneous equations. Math. Comput 19, 577–593 (1965)
    Article MATH MathSciNet Google Scholar
  5. Liu, Z., Zheng, Q., Zhao, P.: A variant of Steffensen’s method of fourth-order convergence and its applications. Appl. Math. Comput 216, 1978–1983 (2010)
    Article MATH MathSciNet Google Scholar
  6. Sharma, J.R., Arora, H.: An efficient derivative free iterative method for solving systems of nonlinear equations. Appl. Anal. Discrete Math 7, 390–403 (2013)
    Article MATH MathSciNet Google Scholar
  7. Wang, X., Zhang, T.: A family of steffensen type methods with seventh-order convergence. Numer. Algor 2, 429–444 (2013)
    Article Google Scholar
  8. Grau-Sánchez, M., Noguera, M., Amat, S.: On the approximation of derivatives using divided difference operators preserving the local convergence order of iterative methods. J. Comput. Appl. Math 237, 263–272 (2013)
    Article Google Scholar
  9. Grau-Sánchez, M., Grau, À., Noguera, M.: Frozen divided difference scheme for solving systems of nonlinear equations. J. Comput. Appl. Math 235, 1739–1743 (2011)
    Article MATH MathSciNet Google Scholar
  10. Ezquerro, J.A., Hernández, M.A., Romero, N.: Solving nonlinear integral equations of Fredholm type with high order iterative methods. J. Comput. Appl. Math 36, 1449–1463 (2011)
    Article Google Scholar
  11. Ezquerro, J.A., Grau, À., Grau-Sánchez, M., Hernández, M.A., Noguera, M.: Analysing the efficiency of some modifications of the secant method. Comput. Math. Appl 64, 2066–2073 (2012)
    Article MATH MathSciNet Google Scholar
  12. Grau-Sánchez, M., Noguera, M.: A technique to choose the most efficient method between secant method and some variants. Appl. Math. Comput 218, 6415–6426 (2012)
    Article MATH MathSciNet Google Scholar
  13. Fousse, L., Hanrot, G., Lefèvre, V., Pélissier, P., Zimmermann, P.: MPFR: a multiple-precision binary floating-point library with correct rounding. ACM Trans. Math. Softw 33, 15–16 (2007)
    Article Google Scholar
  14. http://www.mpfr.org/mpfr.org/mpfr-2.1.0/timings.html
  15. Grau-Sánchez, M., Noguera, M., Gutiérrez, J.M.: On some computational orders of convergence. Appl. Math. Lett 23, 472–478 (2010)
    Article MATH MathSciNet Google Scholar
  16. Amat, S., Busquier, S., Grau, À., Grau-Sánchez, M.: Maximum efficiency for a family of Newton-like methods with frozen derivatives and some applications. Appl. Math. Comput. 219, 7954–7963 (2013)
    Article MATH MathSciNet Google Scholar
  17. Sharma, J.R., Arora, H.: On efficient weighted-Newton methods for solving systems of nonlinear equations. Appl. Math. Comput. 222, 497–506 (2013)
    Article MathSciNet Google Scholar
  18. Potra, F.-A., Pták, V.: Nondiscrete Induction and Iterative Processes. Pitman Publishing, Boston (1984)
    MATH Google Scholar

Download references