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On an Efficient Family of Simultaneous Methods for Finding Polynomial Multiple Zeros

In: Numerical Mathematics and Advanced Applications 2011

Author

Listed:
  • J. Džunić

    (University of Niš, Faculty of Electronic Engineering, Department of Mathematics)

  • M. S. Petković

    (University of Niš, Faculty of Electronic Engineering, Department of Mathematics)

  • L. D. Petković

    (University of Niš, Faculty of Mechanical Engineering, Department of Mathematics)

Abstract

An iterative method for the simultaneous determination of multiple zeros of algebraic polynomials is stated. This method is more efficient compared to all existing simultaneous methods based on fixed point relations. To attain very high computational efficiency, a suitable correction resulting from Li-Liao-Cheng’s two-point fourth-order method of low computational complexity is applied. The presented convergence analysis shows that the convergence rate of the basic method is increased from three to six using this special type of correction and applying only ν additional polynomial evaluations per iteration, where ν is the number of distinct zeros. Computational aspects and some numerical examples are given to demonstrate high computational efficiency and very fast convergence of the proposed method.

Suggested Citation

  • J. Džunić & M. S. Petković & L. D. Petković, 2013. "On an Efficient Family of Simultaneous Methods for Finding Polynomial Multiple Zeros," Springer Books, in: Andrea Cangiani & Ruslan L. Davidchack & Emmanuil Georgoulis & Alexander N. Gorban & Jeremy Levesley (ed.), Numerical Mathematics and Advanced Applications 2011, edition 127, pages 149-156, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-33134-3_16
    DOI: 10.1007/978-3-642-33134-3_16
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