Weight functions for Chebyshev quadrature
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- by Yuan Xu PDF
- Math. Comp. 53 (1989), 297-302 Request permission
Abstract:
In this paper, we investigate if the weight function ${(1 - {x^2})^{ - 1/2}}R(x)$, where $R(x)$ is a rational function of order (1,1), admits Chebyshev quadratures. Many positive examples are provided. In particular, we have proved that the answer is affirmative if $R(x) = 1 + bx$, $|b| < 0.27846 \ldots$.References
- Paul F. Byrd and Lawrence Stalla, Chebyshev quadrature rules for a new class of weight functions, Math. Comp. 42 (1984), no. 165, 173–181. MR 725992, DOI 10.1090/S0025-5718-1984-0725992-1
- Klaus-Jürgen Förster, On weight functions admitting Chebyshev quadrature, Math. Comp. 49 (1987), no. 179, 251–258. MR 890266, DOI 10.1090/S0025-5718-1987-0890266-8
- Walter Gautschi, Advances in Chebyshev quadrature, Numerical analysis (Proc. 6th Biennial Dundee Conf., Univ. Dundee, Dundee, 1975) Lecture Notes in Math., Vol. 506, Springer, Berlin, 1976, pp. 100–121. MR 0468117
- Ja. L. Geronimus, Čebyšev’s quadrature formula, Izv. Akad. Nauk SSSR Ser. Mat. 33 (1969), 1182–1207 (Russian). MR 0259454
- Ja. L. Geronīmus and A. K. Medvedeva, The validity of the “ČebyŠev rule” for a certain two-parameter family of weight functions, Dokl. Akad. Nauk SSSR 224 (1975), no. 3, 516–518 (Russian). MR 0402365
- David K. Kahaner, On equal and almost equal weight quadrature formulas, SIAM J. Numer. Anal. 6 (1969), 551–556. MR 286279, DOI 10.1137/0706049
- Franz Peherstorfer, Weight functions which admit Tchebycheff quadrature, Bull. Austral. Math. Soc. 26 (1982), no. 1, 29–37. MR 679918, DOI 10.1017/S0004972700005578
- J. L. Ullman, A class of weight functions that admit Tchebycheff quadrature, Michigan Math. J. 13 (1966), 417–423. MR 205463
Additional Information
- © Copyright 1989 American Mathematical Society
- Journal: Math. Comp. 53 (1989), 297-302
- MSC: Primary 65D32
- DOI: https://doi.org/10.1090/S0025-5718-1989-0970703-2
- MathSciNet review: 970703