雅可比多项式的线性组合的Lobatto和Radau正求积公式
Lobatto and Radau positive quadrature formulas for linear combinations of Jacobi polynomials
摘要：
对于给定的$θ\in (-1,1)$，我们找出所有参数$α,β\in \{0,1\}$，使得存在一个雅可比多项式$J_{n+1}^{(α,β)}(x)-C J_{n}^{(α,β)}(x)$的线性组合，它产生一个精确度为\textcolor{red}{$2n+2$ ($2n+1$)}的Lobatto（Radau）正求积公式，并包含点$θ$作为节点.这些正求积式在研究单侧多项式$L_1$逼近问题时是非常有用的。
英文摘要：
For a given $θ\in (-1,1)$, we find out all parameters $α,β\in \{0,1\}$ such that, there exists a linear combination of Jacobi polynomials $J_{n+1}^{(α,β)}(x)-C J_{n}^{(α,β)}(x)$ which generates a Lobatto (Radau) positive quadrature formula of degree of exactness \textcolor{red}{$2n+2$ ($2n+1$)} and contains the point $θ$ as a node. These positive quadratures are very useful in studying problems in one-sided polynomial $L_1$ approximation.
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