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Remarks on the Gauss-Lobatto quadrature formula. (Chinese. English summary) Zbl 1199.41171

Summary: It is well known that the Gauss-Lobatto quadrature rule is exact for polynomials of degree at most \(2n-1\). Recently some researchers improved such a quadrature and further minimized the error by means of using integral bounds as additional variables, and offered some numerical examples for monomials of degree up to \(2n+1\), but neither analyzed the error bounds nor restricted the length of the integral interval. In this paper, an upper error bound for such improvements is given. Such an error bound vanishes as the length of the integral interval approaches zero, which shows that their improvement is actually improper.

MSC:

41A55 Approximate quadratures
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