A note on the improved derivative free root-solvers |
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Authors: | Lidija Z. Rančić Miodrag S. Petković |
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Affiliation: | Faculty of Electronic Engineering, University of Niš, P. O. Box 73, 18000 Niš, Serbia |
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Abstract: | Using a fixed point relation of the square-root type and the basic fourth-order method, improved methods of fifth and sixth order for the simultaneous determination of simple zeros of a polynomial are obtained. An increase in convergence is achieved without additional numerical operations, which points to high computational efficiency of the accelerated methods. The main aim of this work is the convergence analysis of improved simultaneous methods given under computationally verifiable initial conditions in the spirit of Smale’s point estimation theory. |
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Keywords: | Zeros of polynomial Simultaneous methods Guaranteed convergence Convergence rate Initial convergence conditions |
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