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