论文标题
在多项式插值中
On polynomial interpolation in the monomial basis
论文作者
论文摘要
在本文中，我们表明，只要Vandermonde矩阵的条件数小于机器epsilon的倒数，因此单一基础通常与插值的条件良好的多项式基础一样好。这导致了使用单个基础上的一般区域对一般区域的分段多项式插值的实用算法。我们的分析还为任意Vandermonde矩阵的状况数量产生了新的上限，该矩阵概括了以前的几个结果。
In this paper, we show that the monomial basis is generally as good as a well-conditioned polynomial basis for interpolation, provided that the condition number of the Vandermonde matrix is smaller than the reciprocal of machine epsilon. This leads to a practical algorithm for piecewise polynomial interpolation over general regions in the complex plane using the monomial basis. Our analysis also yields a new upper bound for the condition number of an arbitrary Vandermonde matrix, which generalizes several previous results.
