隐紧缩寻根
Root-finding with Implicit Deflation
摘要：
函数迭代，如牛顿迭代，是多项式求根的常用工具。我们考虑现实情况，其中一些（例如，条件更好的）根已经被近似，并且其中进一步的计算针对剩余根的近似。这种情况也是现实的根源，通过细分。一个自然的方法，应用显式紧缩已经研究了很多，最近提出的作者之一，本文，但目前我们有助于应用隐式紧缩的替代方法，我们结合映射的变量和反转的输入多项式。我们还展示了另一个未探索的方向，在这个长期和广泛研究的领域取得实质性的进一步进展。也就是说，我们显着提高他们的本地效率的多点多项式评估和快速多极子方法的快速算法的结合。
英文摘要：
Functional iterations such as Newton's are a popular tool for polynomial root-finding. We consider realistic situation where some (e.g., better-conditioned) roots have already been approximated and where further computations is directed to approximation of the remaining roots. Such situation is also realistic for root-finding by means of subdivision. A natural approach of applying explicit deflation has been much studied and recently advanced by one of the authors of this paper, but presently we contribute to the alternative approach of applying implicit deflation, which we combine with mapping the variable and reversion of an input polynomial. We also show another unexplored direction for substantial further progress in this long and extensively studied area. Namely we dramatically increase their local efficiency by means of the incorporation of fast algorithms for multipoint polynomial evaluation and Fast Multipole Method.
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。
