On semicardinal quadrature formulae

Schoenberg, I. J.; Silliman, S. D.

doi:10.1090/S0025-5718-1974-0341825-3

On semicardinal quadrature formulae
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by I. J. Schoenberg and S. D. Silliman PDF

Math. Comp. 28 (1974), 483-497 Request permission

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

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I. J. Schoenberg, Cardinal interpolation and spline functions, J. Approximation Theory 2 (1969), 167–206. MR 257616, DOI 10.1016/0021-9045(69)90040-9
I. J. Schoenberg, Cardinal interpolation and spline functions. VI. Semi-cardinal interpolation and quadrature formulae, J. Analyse Math. 27 (1974), 159–204. MR 493057, DOI 10.1007/BF02788646
I. J. Schoenberg, Cardinal spline interpolation, Conference Board of the Mathematical Sciences Regional Conference Series in Applied Mathematics, No. 12, Society for Industrial and Applied Mathematics, Philadelphia, Pa., 1973. MR 0420078
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