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The Location of the Zeros of the Higher Order Derivatives of a Polynomial

Proceedings of the American Mathematical Society / v.127 no.5. 1999, pp.1493-1497

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Abstract : Let p(z) be a complex polynomial of degree n having k zeros in a disk D. We deal with the problem of finding the smallest concentric disk containing k - l zeros of p $^{(l)}$ (z). We obtain some estimates on the radius of this disk in general as well as in the special case, where k zeros in D are isolated from the other zeros of p(z). We indicate an application to the root-finding algorithms.

Keyword : Primary 30C15 . Secondary 65E05

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