Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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THE MEAN-SQUARE ERROR BOUNDS FOR THE GAUSSIAN QUADRATURE OF ANALYTIC FUNCTIONS

  • Ko, Kwan-Pyo (Department of Computer Engineering Dongseo University ) ;
  • Park, U-Jin (Department of Mathematics Korea Advanced Institute of Science and Technology )
  • Published : 1997.05.01
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Abstract

In this paper we present the $L^2$-estimation for the kernel $K_n$ of the remaider term for the Gaussian quadrature with respect to one of four Chebyshev weight functions and the error bound of the type on the contour $$ $\mid$R_n(f)$\mid$ \leq \frac{2\pi}{\sqrt{l(\Gamma)}} max_{z\in\Gamma}$\mid$f(z)$\mid$ (\smallint_\Gamma $\mid$K_n(z)$\mid$^2$\mid$dz$\mid$)^\frac{2}{1}, $$ where $l(\Gamma)$ denotes the length of the contour $\Gamma$.

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