Pellet定理及相关定理的几何方面
Geometric aspects of Pellet's and related theorems
AI总结：
本文通过线性代数工具改进Pellet定理，用lemniscate提供更精确的零点定位，并推广Cauchy的零点包含区域。
摘要：
Pellet定理确定了多项式零点能否根据模数分成两个区域。我们改进其中一个区域，用lemniscate的闭合内部提供更精确的零点位置信息。此外，Pellet定理被视为Cauchy零点包含区域的推广。利用线性代数工具，我们推导出另一种推广，得到一系列更小的包含区域，这些区域也是lemniscate的闭合内部。
英文摘要：
Pellet's theorem determines when the zeros of a polynomial can be separated into two regions, according to their moduli. We refine one of those regions and replace it with the closed interior of a lemniscate that provides more precise information on the location of the zeros. Moreover, Pellet's theorem is considered the generalization of a zero inclusion region due to Cauchy. Using linear algebra tools, we derive a different generalization that leads to a sequence of smaller inclusion regions, which are also the closed interiors of lemniscates.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
