Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



On a theorem of C. Posse concerning Gaussian quadrature of Chebyshev type

Author: Klaus-Jürgen Förster
Journal: Math. Comp. 62 (1994), 719-724
MSC: Primary 65D32; Secondary 41A55
MathSciNet review: 1219703
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • [1] L. A. Anderson and W. Gautschi, Optimal weighted Chebyshev type quadrature formulas, Calcolo 12 (1975), 211-248. MR 0423764 (54:11738)
  • [2] R. P. Bailey, Convergence of sequences of positive linear functional operations, Duke Math. J. 2 (1936), 287-303. MR 1545924
  • [3] P. L. Chebyshev, Sur les quadratures, J. Math. Pures Appl. (2) 19 (1874), 19-34.
  • [4] K.-J. Förster and G. P. Ostermeyer, On weighted Chebyshev-type quadrature formulas, Math. Comp. 46 (1986), 591-599. MR 829628 (87h:65042)
  • [5] K.-J. Förster, On the minimal variance of quadrature formulas, Numerical Integration III (H. Braßand G. Hämmerlin, eds.), Birkhäuser, Basel, 1988, pp. 37-48. MR 1021521 (91e:65040)
  • [6] W. Gautschi, Advances in Chebyshev quadrature, Numerical Analysis (G. A. Watson, ed.), Lecture Notes in Math., vol. 506, Springer-Verlag, Berlin and New York, 1977, pp. 100-121. MR 0468117 (57:7956)
  • [7] S. E. Notaris, On Gauss-Kronrod quadrature formulae of Chebyshev type, Math. Comp. 58 (1992), 745-753. MR 1122074 (92h:65041)
  • [8] F. Peherstorfer, On Tchebycheff quadrature formulas, Numerical Integration III (H. Braßand G. Hämmerlin, eds.), Birkhäuser, Basel, 1988, pp. 172-186. MR 1021533 (91c:65021)
  • [9] -, Gauss-Tschebycheff quadratures formulas, Numer. Math. 58 (1990), 273-281. MR 1075158 (91j:65052)
  • [10] O. Perron, Algebra, de Gruyter, Berlin, 1932.
  • [11] C. Posse, Sur les quadratures, Nouv. Ann. Math. (2) 14 (1875), 49-62.
  • [12] R. Radau, Sur les formules de quadrature à coefficients égaux, C.R. Acad. Sci. Paris 90 (1880), 520-523.

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 65D32, 41A55

Retrieve articles in all journals with MSC: 65D32, 41A55

Additional Information

Keywords: Chebyshev quadrature, Gaussian quadrature, Gauss-Kronrod quadrature
Article copyright: © Copyright 1994 American Mathematical Society

American Mathematical Society