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On semicardinal quadrature formulae


Authors: I. J. Schoenberg and S. D. Silliman
Journal: Math. Comp. 28 (1974), 483-497
MSC: Primary 65D30
DOI: https://doi.org/10.1090/S0025-5718-1974-0341825-3
MathSciNet review: 0341825
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Abstract: The present paper concerns the semicardinal quadrature formulae introduced in Part III of the reference [3]. These were the limiting forms of Sard's best quadrature formulae as the number of nodes increases indefinitely. Here we give a new derivation and characterization of these formulae. This derivation uses appropriate generating functions and also allows us to compute the coefficients very accurately.


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

  • [1] I. J. Schoenberg, Cardinal interpolation and spline functions, J. Approximation Theory 2 (1969), 167–206. MR 0257616
  • [2] I. J. Schoenberg, Cardinal interpolation and spline functions, J. Approximation Theory 2 (1969), 167–206. MR 0257616
  • [3] I. J. Schoenberg, Cardinal interpolation and spline functions. VI. Semi-cardinal interpolation and quadrature formulae, J. Analyse Math. 27 (1974), 159–204. MR 0493057, https://doi.org/10.1007/BF02788646
    I. J. Schoenberg, Cardinal interpolation and spline functions. VII. The behavior of cardinal spline interpolants as their degree tends to infinity, J. Analyse Math. 27 (1974), 205–229. MR 0493058, https://doi.org/10.1007/BF02788647
    Carl de Boor and I. J. Schoenberg, Cardinal interpolation and spline functions. VIII. The Budan-Fourier theorem for splines and applications, Spline functions (Proc. Internat. Sympos., Karlsruhe, 1975) Springer, Berlin, 1976, pp. 1–79. Lecture Notes in Math., Vol. 501. MR 0493059
  • [4] I. J. Schoenberg, Cardinal spline interpolation, Society for Industrial and Applied Mathematics, Philadelphia, Pa., 1973. Conference Board of the Mathematical Sciences Regional Conference Series in Applied Mathematics, No. 12. MR 0420078
  • [5] I. J. Schoenberg and S. D. Silliman, On semi-cardinal quadrature formulae, Approximation theory (Proc. Internat. Sympos., Univ. Texas, Austin, Tex., 1973) Academic Press, New York, 1973, pp. 461–467. MR 0393974
  • [6] S. D. Silliman, "On complete semi-cardinal quadrature formulae." (To appear.)

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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1974-0341825-3
Article copyright: © Copyright 1974 American Mathematical Society