Abstract
Using Newton’s and Halley’s corrections new simultaneous methods for solving polynomial equations, based on classical Laguerre’s method, are obtained. The convergence order of the proposed methods is five and six, respectively. Further improvements of these methods are accomplished by applying the Gauss-Seidel approach. The lower bounds of the R-order of convergence of the accelerated (single- step) methods are derived. Faster convergence of all proposed methods is attained without additional operations, which provides a high computational efficiency of these methods. Convergence analysis and numerical results are given.
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Petković, M.S., Petković, L., Živković, D. (2001). Laguerre-like Methods for the Simultaneous Approximation of Polynomial Zeros. In: Alefeld, G., Chen, X. (eds) Topics in Numerical Analysis. Computing Supplementa, vol 15. Springer, Vienna. https://doi.org/10.1007/978-3-7091-6217-0_15
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DOI: https://doi.org/10.1007/978-3-7091-6217-0_15
Publisher Name: Springer, Vienna
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