黎曼-斯蒂尔切斯积分的两点Gauss-Legendre Quadrature规则
Two point Gauss-Legendre Quadrature Rule for Riemann-Stieltjes integrals
摘要：
为了用$2$ -点高斯求积规则来逼近黎曼-斯蒂尔切斯积分$\int_a^b {f\left( t \right)dg\left( t \right)}$，我们引入了求积规则\begin{align*} \int_{ - 1}^1 {f\left( t \right)dg\left( t \right)} \approx A f\left( { - \frac{\sqrt 3 }{3}} \right) + B f\left( {\frac{\sqrt 3 }{3}} \right), \end{align*}，以便适当地选择$A$和$B$ .在各种假设下，这种近似的误差估计所涉及的功能提供。
英文摘要：
In order to approximate the Riemann--Stieltjes integral $\int_a^b {f\left( t \right)dg\left( t \right)}$ by $2$--point Gaussian quadrature rule, we introduce the quadrature rule \begin{align*} \int_{ - 1}^1 {f\left( t \right)dg\left( t \right)} \approx A f\left( { - \frac{\sqrt 3 }{3}} \right) + B f\left( {\frac{\sqrt 3 }{3}} \right), \end{align*} for suitable choice of $A$ and $B$. Error estimates for this approximation under various assumptions for the functions involved are provided as well.
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。
