On the convergence condition of generalized root iterations for the inclusion of polynomial zeros
Using a fixed point relation based on the logarithmic derivative of the k-th order of an algebraic polynomial and the definition of the k-th root of a disk, a family of interval methods for the simultaneous inclusion of complex zeros in circular complex arithmetic was established by Petkovic [M.S. Petkovic, On a generalization of the root iterations for polynomial complex zeros in circular interval arithmetic, Computing 27 (1981) 37-55]. In this paper we give computationally verifiable initial conditions that guarantee the convergence of this parallel family of inclusion methods. These conditions are significantly relaxed compared to the previously stated initial conditions presented in literature. (C) 2007 IMACS. Published by Elsevier B.V. All rights reserved.
convergence conditions polynomial zeros circular interval arithmetic inclusion methods simultaneous methods