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Journal of Applied Mathematics
Volume 2012, Article ID 709832, 11 pages
http://dx.doi.org/10.1155/2012/709832
Research Article

The Point Zoro Symmetric Single-Step Procedure for Simultaneous Estimation of Polynomial Zeros

1Department of Mathematics, Faculty of Science, Universiti Putra Malaysia, 43400 UPM Serdang, Selangor, Malaysia
2School of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, 43600 Bangi, Selangor, Malaysia

Received 15 November 2011; Revised 29 February 2012; Accepted 20 March 2012

Academic Editor: Martin Weiser

Copyright © 2012 Mansor Monsi et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. L. W. Ehrlich, “A modified Newton method for polynomials,” Communications of the ACM, vol. 10, pp. 107–108, 1967. View at Google Scholar
  2. O. Aberth, “Iteration methods for finding all zeros of a polynomial simultaneously,” Mathematics of Computation, vol. 27, pp. 339–344, 1973. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  3. G. Alefeld and J. Herzberger, “On the convergence speed of some algorithms for the simultaneous approximation of polynomial roots,” SIAM Journal on Numerical Analysis, vol. 11, pp. 237–243, 1974. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  4. M. R. Farmer and G. Loizou, “A class of iteration functions for improving, simultaneously, approximations to the zeros of a polynomial,” vol. 15, no. 3, pp. 250–258, 1975. View at Google Scholar · View at Zentralblatt MATH
  5. G. V. Milovanović and M. S. Petković, “On the convergence order of a modified method for simultaneous finding polynomial zeros,” Computing, vol. 30, no. 2, pp. 171–178, 1983. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  6. M. S. Petković and L. V. Stefanović, “On a second order method for the simultaneous inclusion of polynomial complex zeros in rectangular arithmetic,” Computing. Archives for Scientific Computing, vol. 36, no. 3, pp. 249–261, 1986. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  7. O. Kerner, “Total step procedure for the calculation of the zeros of polynomial,” Numerische Mathematik, vol. 8, pp. 290–294, 1966. View at Google Scholar
  8. M. Monsi and M. A. Wolfe, “Interval versions of some procedures for the simultaneous estimation of complex polynomial zeros,” Applied Mathematics and Computation, vol. 28, no. 3, pp. 191–209, 1988. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  9. M. Monsi, “The point symmetric single-step PSS1 procedure for simultaneous approximation of polynomial zeros,” Malaysian Journal of Mathematical Sciences, vol. 6, no. 1, pp. 29–46, 2012. View at Google Scholar
  10. S. F. Rusli, M. Monsi, M. A. Hassan, and W. J. Leong, “On the interval zoro symmetric single-step procedure for simultaneous finding of real polynomial zeros,” Applied Mathematical Sciences, vol. 5, no. 75, pp. 3693–3706, 2011. View at Google Scholar
  11. A. C. Aitken, “Studies in practical mathematics. V. On the iterative solution of a system of linear equations,” Proceedings of the Royal Society of Edinburgh A, vol. 63, pp. 52–60, 1950. View at Google Scholar · View at Zentralblatt MATH
  12. G. Alefeld and J. Herzberger, Introduction to Interval Computations, Computer Science and Applied Mathematics, Academic Press, New York, NY, USA, 1983.
  13. J. M. Ortega and W. C. Rheinboldt, Iterative Solution of Nonlinear Equations in Several Variables, Academic Press, New York, NY, USA, 1970.