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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.

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  • [1] I. J. Schoenberg, "Cardinal interpolation and spline functions," J. Approximation Theory, v. 2, 1969, pp. 167-206. MR 41 #2266. MR 0257616 (41:2266)
  • [2] I. J. Schoenberg, "Cardinal interpolation and spline functions. IV. The exponential Euler splines," in Linear Operators and Approximation, edited by P. L. Butzer, J.-P. Kahane and B. Sz.-Nagy, Proceedings of the Conference (Oberwolfach, Aug. 14-22, 1971), ISNM, v. 20, 1972, pp. 382-404. MR 0257616 (41:2266)
  • [3] I. J. Schoenberg, Cardinal Interpolation and Spline Functions. VI. Semi-Cardinal Interpolation and Quadrature Formulae, MRC T.S. Report #1180, Madison, Wisconsin, 1971; J. Analyse Math. (To appear.) MR 0493057 (58:12097a)
  • [4] I. J. Schoenberg, Cardinal Spline Interpolation, CBMS Regional Conference Monograph, no. 12, SIAM, Philadelphia, 1973. MR 0420078 (54:8095)
  • [5] I. J. Schoenberg & S. D. Silliman, On Semi-Cardinal Quadrature Formula, MRC T.S. Report #1300, Madison, Wisconsin, October 1972. MR 0393974 (52:14781)
  • [6] S. D. Silliman, "On complete semi-cardinal quadrature formulae." (To appear.)

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Article copyright: © Copyright 1974 American Mathematical Society

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