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
- 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, 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 S. D. Silliman, "On complete semi-cardinal quadrature formulae." (To appear.)
Additional Information
- © Copyright 1974 American Mathematical Society
- Journal: Math. Comp. 28 (1974), 483-497
- MSC: Primary 65D30
- DOI: https://doi.org/10.1090/S0025-5718-1974-0341825-3
- MathSciNet review: 0341825