A general semilocal convergence theorem for simultaneous methods for polynomial zeros and its applications to Ehrlich’s and Dochev–Byrnev’s methods

摘要

In this paper, we establish a general semilocal convergence theorem (withcomputationally verifiable initial conditions and error estimates) foriterative methods for simultaneous approximation of polynomial zeros. Asapplication of this theorem, we provide new semilocal convergence results forEhrlich's and Dochev-Byrnev's root-finding methods. These results improve theresults of Petkovi'c, Herceg and Ili'c [Numer. Algorithms 17 (1998) 313--331]and Proinov [C.~R. Acad. Bulg. Sci. 59 (2006) 705--712]. We also prove thatDochev-Byrnev's method (1964) is identical to Pre{ s}i'c-Tanabe's method(1972).