A theorem for separating close roots of a polynomial and its derivatives

Authors:
Tateaki Sasaki
Affiliations:
University of Tsukuba, Tsukuba-shi, Ibaraki, Japan
Venue:
ACM SIGSAM Bulletin
Year:
2004

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Abstract

Let P(z) be a univariate polynomial over C, having m close roots around the origin. We present a theorem which separates a cluster of m - k close roots of dk P/dzk around the origin from the other roots, where 0 ≤ k m. We compare our theorem with those of Marden-Walsh and Yakoubsohn, and show superiority of our theorem.