Figure - available from: Numerical Algorithms
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RLCs bounded by the white curves, of the S2-m formula of order m = 32 (left) and the Voronoi diagram (right) for four zeros 2i, 1, − i and − 1 of a polynomial (z − 2i)(z − 1)²(z + i)³(z + 1)⁵
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It is known that the immediate basins of attraction of zeros of a complex polynomial f(z) with simple zeros under the iteration of family of iterations, i.e., Schröder’s formula of the second kind (König’s formula or the Basic Family) with the convergence degree m ≥ 2, converge to the Voronoi diagram of the zeros as \(m\to \infty \). In a previous...
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For a univariate real polynomial without zero coefficients, Descartes' rule of signs (completed by an observation of Fourier) says that its numbers $pos$ of positive and $neg$ of negative roots (counted with multiplicity) are majorized respectively by the numbers $c$ and $p$ of sign changes and sign preservartions in the sequence of its coefficient...
