On the guaranteed convergence of a cubically convergent Weierstrass-like root-finding method |
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| Authors: | Miodrag S Petkovi? Lidija Z Ran?i? |
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| Affiliation: | 1. Department of Mathematics, Faculty of Electronic Engineering, University of Ni?, 18000 Ni?, Serbiamsp@junis.ni.ac.rs;3. Department of Mathematics, Faculty of Electronic Engineering, University of Ni?, 18000 Ni?, Serbia |
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| Abstract: | Initial conditions that provide guaranteed and fast convergence of the Weierstrass-like cubically convergent iterative method for the simultaneous determination of all simple zeros of a polynomial are considered. It is proved that this method is convergent under suitable conditions stated in the spirit of Smale's point estimation theory. The proposed convergence conditions are computationally verifiable since they depend only on initial approximations and the degree of a given polynomial, which is of practical importance. |
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| Keywords: | iterative methods polynomial roots initial conditions guaranteed convergence simultaneous methods |
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