Error bounds for Gauss-Radau and Gauss-Lobatto rules of analytic functions

Commun. Korean Math. Soc. 1997 Vol. 12, No. 3, 797-812

Kwan Pyo Ko Dongseo University

Abstract : For analytic functions we give an expression for the kernel $K_n$ of the remainder terms for the Gauss--Radau and the Gauss--Lobatto rules with end points of multiplicity $r$ and prove the convergence of the kernel we obtained. The error bound are obtained for the type $|R_n(f)|\le \frac1{2\pi}l(\Gamma)\max\Sb{z\in\Gamma}\endSb |K_n(z)|\max\Sb{z\in\Gamma}\endSb|f(z)|$, where $l(\Gamma)$ denotes the length of contour $\Gamma$.

Keywords : Gaussian quadrature, orthogonal polynomial. This work was partially supported by the Dongseo University Research Fund