Semilocal convergence of two iterative methods for simultaneous computation of polynomial zeros

Details Semilocal convergence of two iterative methods for simultaneous computation of polynomial zeros Semilocal convergence of two iterative methods for simultaneous computation of polynomial zeros

2007-09-07

arxiv.org/abs/0709.1068v1

C. R. Acad. Bulg. Sci 59 (2006), No 7, 705--712

Mathematics

Numerical Analysis

11 pages

Scientific paper

In this paper we study some iterative methods for simultaneous approximation of polynomial zeros. We give new semilocal convergence theorems with error bounds for Ehrlich's and Nourein's iterations. Our theorems generalize and improve recent results of Zheng and Huang [J. Comput. Math. 18 (2000), 113--122], Petkovi\'c and Herceg [J. Comput. Appl. Math. 136 (2001), 283--307] and Nedi\'c [Novi Sad J. Math. 31 (2001), 103--111]. We also present a new sufficient condition for simple zeros of a polynomial.

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