On a theorem of C. Posse concerning Gaussian quadrature of Chebyshev type
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- by Klaus-Jürgen Förster PDF
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Abstract:
We consider (n, m) Chebyshev formulae of algebraic degree m using n nodes. The aim of this short note is to show that by a simple algebraic method C. Posse’s theorem concerning Gaussian quadrature of Chebyshev type can be improved. Furthermore, we given an application of this method to Gauss-Kronrod quadrature of Chebyshev type.References
- L. A. Anderson and W. Gautschi, Optimal weighted Chebyshev-type quadrature formulas, Calcolo 12 (1975), no. 3, 211–248. MR 423764, DOI 10.1007/BF02576818
- R. P. Bailey, Convergence of sequences of positive linear functional operations, Duke Math. J. 2 (1936), no. 2, 287–303. MR 1545924, DOI 10.1215/S0012-7094-36-00224-7 P. L. Chebyshev, Sur les quadratures, J. Math. Pures Appl. (2) 19 (1874), 19-34.
- Klaus-Jürgen Förster and Georg-Peter Ostermeyer, On weighted Chebyshev-type quadrature formulas, Math. Comp. 46 (1986), no. 174, 591–599, S21–S27. MR 829628, DOI 10.1090/S0025-5718-1986-0829628-2
- Klaus-Jürgen Förster, On the minimal variance of quadrature formulas, Numerical integration, III (Oberwolfach, 1987) Internat. Schriftenreihe Numer. Math., vol. 85, Birkhäuser, Basel, 1988, pp. 37–48. MR 1021521, DOI 10.1007/978-3-0348-6398-8_{4}
- 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
- Sotirios E. Notaris, On Gauss-Kronrod quadrature formulae of Chebyshev type, Math. Comp. 58 (1992), no. 198, 745–753. MR 1122074, DOI 10.1090/S0025-5718-1992-1122074-9
- Franz Peherstorfer, On Tchebycheff quadrature formulas, Numerical integration, III (Oberwolfach, 1987) Internat. Schriftenreihe Numer. Math., vol. 85, Birkhäuser, Basel, 1988, pp. 172–185. MR 1021533, DOI 10.1007/978-3-0348-6398-8_{1}6
- Franz Peherstorfer, Gauss-Tchebycheff quadrature formulas, Numer. Math. 58 (1990), no. 3, 273–286. MR 1075158, DOI 10.1007/BF01385625 O. Perron, Algebra, de Gruyter, Berlin, 1932. C. Posse, Sur les quadratures, Nouv. Ann. Math. (2) 14 (1875), 49-62. R. Radau, Sur les formules de quadrature à coefficients égaux, C.R. Acad. Sci. Paris 90 (1880), 520-523.
Additional Information
- © Copyright 1994 American Mathematical Society
- Journal: Math. Comp. 62 (1994), 719-724
- MSC: Primary 65D32; Secondary 41A55
- DOI: https://doi.org/10.1090/S0025-5718-1994-1219703-X
- MathSciNet review: 1219703