On the convergence order of a modified method for simultaneous finding polynomial zeros |
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Authors: | Dr G V Milovanović Dr M S Petković |
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Affiliation: | 1. Department of Mathematics, Faculty of Electronic Engineering, Beogradska 14, 18000, Ni?, Yugoslavia
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Abstract: | Using Newton's corrections and Gauss-Seidel approach, a modification of single-step method 1] for the simultaneous finding all zeros of ann-th degree polynomial is formulated in this paper. It is shown thatR-order of convergence of the presented method is at least 2(1+τ n ) where τ n ∈(1,2) is the unique positive zero of the polynomial \(\tilde f_n (\tau ) = \tau ^n - \tau - 1\) . Faster convergence of the modified method in reference to the similar methods is attained without additional calculations. Comparison is performed in the example of an algebraic equation. |
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