Two point Gauss-Legendre Quadrature Rule for Riemann-Stieltjes integrals

Abstract

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.

arXiv comment8 pages

References in corpus (1)

• New sharp inequalities of Ostrowski and generalized trapezoid type for the Riemann-Stieltjes integrals and applications

Cited by in corpus (2)

• Lp-error Bounds Of Two And Three-point Quadrature Rules For Riemann-stieltjes Integrals
• Two-Point Quadrature Rules for Riemann-Stieltjes Integrals with Lp-error estimates