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.
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Acknowledgements
This work was supported by the Serbian Ministry of Science under grant 174022.
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Džunić, J., Petković, M.S., Petković, L.D. (2013). On an Efficient Family of Simultaneous Methods for Finding Polynomial Multiple Zeros. In: Cangiani, A., Davidchack, R., Georgoulis, E., Gorban, A., Levesley, J., Tretyakov, M. (eds) Numerical Mathematics and Advanced Applications 2011. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33134-3_16
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DOI: https://doi.org/10.1007/978-3-642-33134-3_16
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