Semilocal convergence of two iterative methods for simultaneous computation of polynomial zeros
For researchers in numerical analysis, the work offers improved theoretical guarantees for existing polynomial root-finding methods, but is incremental.
The paper provides new semilocal convergence theorems with error bounds for Ehrlich's and Nourein's iterative methods for simultaneous polynomial zero approximation, generalizing and improving recent results. It also presents a new sufficient condition for simple zeros.
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], Petković and Herceg [J. Comput. Appl. Math. 136 (2001), 283--307] and Nedić [Novi Sad J. Math. 31 (2001), 103--111]. We also present a new sufficient condition for simple zeros of a polynomial.