Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

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

 

 

Nonexistence of Chebyshev-type quadratures on infinite intervals


Author: Walter Gautschi
Journal: Math. Comp. 29 (1975), 93-99
MSC: Primary 65D30
DOI: https://doi.org/10.1090/S0025-5718-1975-0368392-3
MathSciNet review: 0368392
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Quadrature rules on semi-infinite and infinite intervals are considered involving weight functions of the Laguerre and Hermite type. It is shown that such quadrature rules cannot have equal coefficients and real nodes unless the algebraic degree of accuracy is severely limited.


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

  • [1] L. A. ANDERSON & W. GAUTSCHI, "Optimal weighted Chebyshev-type quadrature formulas" (To be published.)
  • [2] S. BERNSTEIN, "Sur un système d'équations indéterminées," J. Math. Pures Appl., v. 17, 1938, pp. 179-186.
  • [3] Luigi Gatteschi, Sulla non esistenza di certe formule di quadratura, Univ. e Politec. Torino Rend. Sem. Mat. 24 (1964/1965), 157–172 (Italian). MR 0187394
  • [4] V. I. Krylov, Mechanical quadratures with equal coefficients for the integrals ∫^{∞}₀ 𝑒^{-𝑥}𝑓(𝑥)𝑑𝑥 and ∫_{-∞}𝑒^{-𝑥²}𝑓(𝑥)𝑑𝑥, Dokl. Akad. Nauk BSSR 2 (1955), 187–192 (Russian). MR 0109978
  • [5] Herbert E. Salzer, Equally weighted quadrature formulas over semi-infinite and infinite intervals, J. Math. and Phys. 34 (1955), 54–63. MR 0069586, https://doi.org/10.1002/sapm195534154
  • [6] Herbert S. Wilf, The possibility of Tschebycheff quadrature on infinite intervals, Proc. Nat. Acad. Sci. U.S.A. 47 (1961), 209–213. MR 0125380

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 65D30

Retrieve articles in all journals with MSC: 65D30


Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1975-0368392-3
Article copyright: © Copyright 1975 American Mathematical Society