On Gauss-Kronrod quadrature formulae of Chebyshev type

Author:
Sotirios E. Notaris

Journal:
Math. Comp. **58** (1992), 745-753

MSC:
Primary 65D32; Secondary 33C45

DOI:
https://doi.org/10.1090/S0025-5718-1992-1122074-9

MathSciNet review:
1122074

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Abstract: We prove that there is no positive measure 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 , where is even, on a symmetric interval , 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 on for which the Gauss-Kronrod formula has all weights equal if , or has the form for all , is the Chebyshev measure of the first kind .

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1992-1122074-9

Keywords:
Gauss-Kronrod quadrature formulae,
Chebyshev quadrature

Article copyright:
© Copyright 1992
American Mathematical Society