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. We also show that the monomial basis is more advantageous than other polynomial bases in a number of applications.
翻译:在本文中,我们展示了单项式基础通常与良条件的多项式基础一样适用于插值运算,前提是Vandermonde矩阵的条件数小于机器精度的倒数。我们还展示了单项式基础在许多应用中比其他多项式基础更具优势。