On weighted Chebyshev-type quadrature formulas
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- by Klaus-Jürgen Förster and Georg-Peter Ostermeyer PDF
- Math. Comp. 46 (1986), 591-599 Request permission
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 $n \leqslant 25$.References
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Additional Information
- © Copyright 1986 American Mathematical Society
- Journal: Math. Comp. 46 (1986), 591-599
- MSC: Primary 65D32
- DOI: https://doi.org/10.1090/S0025-5718-1986-0829628-2
- MathSciNet review: 829628