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 | References | Similar Articles | Additional Information

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.

**[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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DOI:
https://doi.org/10.1090/S0025-5718-1974-0341825-3

Article copyright:
© Copyright 1974
American Mathematical Society