Applied & computational complex analysis: power series integration conformal mapping location of zero
On Halley-like algorithms for simultaneous approximation of polynomial complex zeros
SIAM Journal on Numerical Analysis
On zero finding methods of higher order from data at one point
Journal of Complexity
Approximate zeros of quadratically convergent algorithms
Mathematics of Computation
Weierstrass formula and zero-finding methods
Numerische Mathematik
The theory of Smale's point estimation and its applications
Proceedings of the international meeting on Linear/nonlinear iterative methods and verification of solution
Ten methods to bound multiple roots of polynomials
Journal of Computational and Applied Mathematics
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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.