A Nonstationary Halley’s Iteration Method by Using Divided Differences Formula

DOI: 10.4236/am.2012.32026   PDF   HTML     4,427 Downloads   7,174 Views   Citations

Abstract

This paper presents a new nonstationary iterative method for solving non linear algebraic equations that does not require the use of any derivative. The study uses only the Newton’s divided differences of first and second orders instead of the derivatives of (1).

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N. Ide, "A Nonstationary Halley’s Iteration Method by Using Divided Differences Formula," Applied Mathematics, Vol. 3 No. 2, 2012, pp. 169-171. doi: 10.4236/am.2012.32026.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1] T. Kogan, L. Sapir and A. Sapir, “A Nonstationary Iterative Second-Order Method for Solving Non- Linear Equations,” Applied Mathematics and Computation, Vol. 188, No. 1, 2007, pp. 75-82. doi:10.1016/j.amc.2006.09.092
[2] T. I. Kogan, “Generalization of the Method of Chords for an Algebraic or Transcendental Equation,” in Russian, Ta?hkent. Gos. Univ. Naun. Trudy Vyp, Vol. 276, 1966, pp. 53-55.
[3] D. K. R. Babajee and M. Z. Dauhoo, “An Analysis of the Properties of the Variants of Newton’s Method with Third Order Convergence,” Applied Mathematics and Computation, Vol. 183, No. 1, 2006, pp. 659-684. doi:10.1016/j.amc.2006.05.116

  
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