Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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ERROR BOUNDS FOR GAUSS-RADAU AND GAUSS-LOBATTO RULES OF ANALYTIC FUNCTIONS

  • Ko, Kwan-Pyo (Computer Engineering Division of System Engineering Dongseo University)
  • Published : 1997.07.01
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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 $$\mid$R_n(f)$\mid$ \leq \frac{1}{\pi}l(\Gamma) max_{z \in \Gamma} $\mid$K_n(z)$\mid$ max_{z \in \Gamma} $\mid$f(z)$\mid$$, where $l(\Gamma)$ denotes the length of contour $\Gamma$.

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References

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