On the Critical Points of Kyurkchiev’s Method for Solving Algebraic Equations

Abstract

This paper is dedicated to Prof. Nikolay Kyurkchiev
on the occasion of his 70th anniversary

This paper gives sufficient conditions for kth approximations of
the zeros of polynomial f (x) under which Kyurkchiev’s method fails on the
next step. The research is linked with an attack on the global convergence
hypothesis of this commonly used in practice method (as correlate hypothesis
for Weierstrass–Dochev’s method). Graphical examples are presented.