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- W1982664761 abstract "An iterative method in parallel mode for the simultaneous determination of multiple roots of algebraic polynomials is stated together with its single-step variant. These methods are more efficient compared to all 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 and Gauss-Seidel?s approach are applied. Considerable increase of the convergence rate is obtained applying only n additional polynomial evaluations per iteration, where n is the number of distinct roots. A special emphasis is given to the convergence analysis and computational efficiency of the proposed methods. The presented convergence analysis shows that the R-order of convergence of the proposed single-step method is at least 2 + ?v; where ?v?2 (4,6) is the unique positive root of the polynomial gv(t) = tn-4n-1 t-22n-1: The convergence order of the corresponding total-step method is six. Computational aspects and some numerical examples are given to demonstrate high computational efficiency and very fast convergence of the proposed methods." @default.
- W1982664761 created "2016-06-24" @default.
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- W1982664761 date "2014-01-01" @default.
- W1982664761 modified "2023-09-24" @default.
- W1982664761 title "On an efficient method for the simultaneous approximation of polynomial multiple roots" @default.
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- W1982664761 doi "https://doi.org/10.2298/aadm140310005p" @default.
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