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Inclusion Weierstrass-like root-finders with corrections

Petković Ljiljana D. (Faculty of Mechanical Engineering, University of Niš)
Petković Miodrag S. (Faculty of Electronic Engineering, University of Niš)
Milošević Dušan M. (Faculty of Electronic Engineering, University of Niš)

In this paper we present iterative methods of Weierstrass's type for the simultaneous inclusion of all multiple zeros of a polynomial. The order of convergence of the proposed interval method is 1 + √2 ≈ 2.414 or 3, depending on the type of the applied disk inversion. The criterion for the choice of a proper circular root-set is given. This criterion uses the already calculated entries which increases the computational efficiency of the presented algorithms. Numerical results are given to demonstrate the convergence behavior.

Keywords: multiple zeros of polynomials, simultaneous inclusion methods, convergence rate, circular arithmetic