On semicardinal quadrature formulae
Authors:
I. J. Schoenberg and S. D. Silliman
Journal:
Math. Comp. 28 (1974), 483497
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.
 [1]
I. J. Schoenberg, "Cardinal interpolation and spline functions," J. Approximation Theory, v. 2, 1969, pp. 167206. 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. 1422, 1971), ISNM, v. 20, 1972, pp. 382404. MR 0257616 (41:2266)
 [3]
I. J. Schoenberg, Cardinal Interpolation and Spline Functions. VI. SemiCardinal 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 SemiCardinal Quadrature Formula, MRC T.S. Report #1300, Madison, Wisconsin, October 1972. MR 0393974 (52:14781)
 [6]
S. D. Silliman, "On complete semicardinal quadrature formulae." (To appear.)
 [1]
 I. J. Schoenberg, "Cardinal interpolation and spline functions," J. Approximation Theory, v. 2, 1969, pp. 167206. 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. 1422, 1971), ISNM, v. 20, 1972, pp. 382404. MR 0257616 (41:2266)
 [3]
 I. J. Schoenberg, Cardinal Interpolation and Spline Functions. VI. SemiCardinal 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 SemiCardinal Quadrature Formula, MRC T.S. Report #1300, Madison, Wisconsin, October 1972. MR 0393974 (52:14781)
 [6]
 S. D. Silliman, "On complete semicardinal quadrature formulae." (To appear.)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718197403418253
PII:
S 00255718(1974)03418253
Article copyright:
© Copyright 1974
American Mathematical Society
