The stability property of representations of interpolation polynomials is measured through a condition number. We analyze the conditioning of the Newton formula for the interpolation polynomial. We show that the conditioning associated to the Newton representation of the interpolant at the first n points of an ℜ-Leja sequence grows at most like $n^5(5\log n-1)$. The main application is the construction of explicit multivariate points in ${[-1,1]}^d$ whose conditioning also grows like a polynomial.

中文翻译：

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关于拉格朗日插值的牛顿公式的条件

插值多项式表示的稳定性是通过条件数来衡量的。我们分析了用于插值多项式的牛顿公式的条件。我们表明，与在ℜ-Leja 序列的前n个点处的插值的牛顿表示相关的条件最多增长为$n^5(5\mathrm{日志}n-1)$. 主要应用是构造显式的多元点${[-1,1]}^d$ 其条件也像多项式一样增长。