连通范德蒙德矩阵的历史及其求逆算法
History of confluent Vandermonde matrices and inverting them algorithms
AI总结：
本文回顾了连通范德蒙德矩阵自1891年以来的历史，并介绍了用于求解线性系统及求逆的算法，特别提供了一个无需符号计算的数值算法。
摘要：
作者受全球研究人员的多次询问启发，撰写此文以提供一种可在二次时间内对任意参数值（包括特征多项式大根多重性）求逆的连通范德蒙德矩阵的实用算法。文章回顾了该特殊矩阵自1891年以来的历史，并调查了用于求解线性系统及求逆的算法。特别地，文章还通过实例展示了不使用符号计算的数值算法，该算法可直接在通用编程语言或特定数学软件包中实现。
英文摘要：
The author was encouraged to write this review by numerous enquiries from researchers all over the world, who needed a ready-to-use algorithm for the inversion of confluent Vandermonde matrices which works in quadratic time for any values of the parameters allowed by the definition, including the case of large root multiplicities of the characteristic polynomial. Article gives the history of the title special matrix since 1891 and surveys algorithms for solving linear systems with the title class matrix and inverting it. In particular, it presents, also by example, a numerical algorithm which does not use symbolic computations and is ready to be implemented in a general-purpose programming language or in a specific mathematical package.
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。
