PUBLICATIONS DE L'INSTITUT MATHÉMATIQUE (BEOGRAD) (N.S.) Vol. 28(42), pp. 158168 (1980) 

A CONVERGENCE THEOREM FOR A METHOD FOR SIMULTANEOUS DETERMINATION OF ALL ZEROS OF A POLYNOMIALMarica D. Presi\'cMatematicki fakultet, Beograd, YugoslaviaAbstract: As it is wellknown the NewtonRaphson method is closely connected with the Taylor polynomial. Using this connection the Ostrowski' fundamental existence theorem for NewtonRaphson method [3], [4] can be proved in an very natural way [6]. The S.B. Presi\'c's method [7] for simultaneuus determination of all roots of polynomial can be obtained using the interpolation formulae of Newton and Lagrange [5]. We use that fact in the convergence theorem which we prove in this paper. We note that the convergence conditions depend only on the intial points of roots, their distances and on the degree of polynomial. Full text of the article:
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© 2001 Mathematical Institute of the Serbian Academy of Science and Arts
