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Mathematics of Computation

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On weighted Chebyshev-type quadrature formulas


Authors: Klaus-Jürgen Förster and Georg-Peter Ostermeyer
Journal: Math. Comp. 46 (1986), 591-599, S21
MSC: Primary 65D32
MathSciNet review: 829628
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Abstract: A weighted quadrature formula is of Chebyshev type if it has equal coefficients and real (but not necessarily distinct) nodes. For a given weight function we study the set $ T(n,d)$ consisting of all Chebyshev-type formulas with n nodes and at least degree d. It is shown that in nonempty $ T(n,d)$ there exist two special formulas having "extremal" properties. This result is used to prove uniqueness and further results for E-optimal Chebyshev-type formulas. For the weight function $ w \equiv 1$, numerical investigations are carried out for $ n \leqslant 25$.


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DOI: https://doi.org/10.1090/S0025-5718-1986-0829628-2
Article copyright: © Copyright 1986 American Mathematical Society