分离多项式及其导数的紧根的定理

SIGSAM Bull. Pub Date : 2004-09-01 DOI:10.1145/1040034.1040039

Tateaki Sasaki

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引用次数: 1

摘要

设P(z)是C上的单变量多项式，在原点周围有m个紧根。在0≤k < m的情况下，给出了dk P/dzk在原点附近的m - k个紧根簇与其他根的分离定理，并与Marden-Walsh和Yakoubsohn的定理进行了比较，证明了该定理的优越性。

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

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 d^k P/dz^k 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.

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SIGSAM Bull.

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