Advertisement

Numerical Algorithms

, Volume 81, Issue 3, pp 1149–1155 | Cite as

On the problem of starting points for iterative methods

  • Ştefan Măruşter
  • Laura MăruşterEmail author
Open Access
Original Paper
  • 217 Downloads

Abstract

We propose an algorithm to find a starting point for iterative methods. Numerical experiments show empirically that the algorithm provides starting points for different iterative methods (like Newton method and its variants) with low computational cost.

Keywords

Iterative methods Starting point Numerical experiments 

References

  1. 1.
    Maruster, S.: The solution by iteration of nonlinear equations in Hilbert spaces. Proc. Amer. Math. Soc. 63, 69–73 (1977)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Baker Kearfott, R.: Abstract generalized bisection and cost bound. Math. Comput. 49(179), 187–202 (1987)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Adler, A.: On the bisection method for triangles. Math. Comput. 40(162), 571–574 (1983)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Xu, Z.-B., Zhang, J.-S., Wang, W.: A cell exclusion algorithm for determining all the solutions of a nonliniar system of equations. Appl. Math. and Comput. 80, 181–208 (1996)MathSciNetzbMATHGoogle Scholar
  5. 5.
    Hansen, E.R., Greenberg, R.I.: An interval Newton method. Appl. Math. Comput. 12(2-3), 89–98 (1983)MathSciNetzbMATHGoogle Scholar
  6. 6.
    Allgower, E.L., Georg, K.: Simplicial and continuation methods for approximating fixed points and solutions to systems of equations. SIAM Rev. 22, 28–85 (1980)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Karra, C.L., Weckb, B., Freemanc, L.M.: Solutions to systems of nonlinear equations via a genetic algorithm. Eng. Appl. Artif. Intel. 11(3), 369–376 (1998)CrossRefGoogle Scholar
  8. 8.
    Rheinboldt, W.C.: An adaptive continuation process for solving systems of nonlinear equations. Polish Acad. Sci. Banach Center Publ. 3, 129–14 (1975)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Catinas, E.: Estimating the radius of an attraction ball. Appl. Math. Lett. 22, 712–714 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Hernández-Veron, M.A., Romero, N.: On the local convergence of a third order family of iterative processes. Algorithms 8, 1121–1128 (2015)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Rus, I.A.: A conjecture on global asymptotic stability, workshop iterative approximation of fixed points. In: 19Th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing, Timisoara (2017)Google Scholar
  12. 12.
    Berinde, V., Maruşter, St., Rus, I.A.: On an open problem regarding the spectral radius of the derivatives of a function and of its iterates (in preparation)Google Scholar
  13. 13.
    Miyajima, S., Kashiwagi, M.: Existence test for solution of nonlinear systems applying affine arithmetic. J. Comput. Appl. Math. 199, 304–309 (2007)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© The Author(s) 2018

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.West University of TimisoaraTimisoaraRomania
  2. 2.University of GroningenGroningenThe Netherlands

Personalised recommendations