On iteration methods without derivatives for the simultaneous determination of polynomial zeros

Carstensen, C. and M.S. PetkoviC, On iteration methods without derivatives for the simultaneous determination of polynomial zeros, Journal of Computational and Applied Mathematics 45 (1993) 251-266. Several algorithms for simultaneously approximating simple complex zeros of a polynomial are presented. These algorithms use Weierstrass’ corrections and do not require any polynomial derivatives. It is shown that Nourein’s method is, actually, regula falsi for Weierstrass’ corrections. Convergence analysis and computational efficiency are given for the considered methods in complex and circular arithmetic. Special attention is paid to hybrid methods that combine the efficiency of floating-point arithmetic and the inclusion property of interval arithmetic.

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