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On Gauss-Kronrod Quadrature Formulae of Chebyshev Type

1992
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Mathematics of Computation
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We prove that there is no positive measure da on (a, b) such that the corresponding Gauss-Kronrod quadrature formula is also a Chebyshev quadrature formula. The same is true if we consider measures of the form do(t) = a(t)dt, where w(t) is even, on a symmetric interval (-a, a), and the Gauss-Kronrod formula is required to have equal weights only for n even. We also show that the only positive and even measure da(t) = da(-t) on (-1, 1) for which the Gauss-Kronrod formula has all weights equal if

doi:10.2307/2153213
fatcat:fi22r7v7nnbclpd6cm7zsvac4m