References
M. Abramowitz and I. A. Stegun (Editors),Handbook of mathematical functions with formulas, graphs, and mathematical tables, National Bureau of Standards, Washington, D.C., 1964.
A. Calderón, F. Spitzer and H. Widom,Inversion of Toeplitz matrices, Illinois J. Math. 3 (1959), 490–498.
Roger Cotes,De metodo differentiali Newtoniana, in the Appendix of Harmonia Mensurarum, Cambridge, 1722.
M. G. Krein,Integral equations on a half-line with kernel depending upon the difference of the arguments, Amer. Math. Soc. Trans. (2) 22 (1962), 163–288.
P. R. Lipow and I. J. Schoenberg,Cardinal interpolation and spline functions III. Cardinal Hermite interpolation, J. Linear Algebra Appl.6 (1973), 273–304. Also MRC Tech. Sum. Rep. #1113.
L. F. Meyers and A. Sard,Best approximate integration formulas, J. Math. and Phys.29 (1950), 118–123.
A. Sard,Linear approximation, American Math. Society, Providence, R. I., 1963.
A. Sard and S. Weintraub,A book of splines J. Wiley and Sons, New York, 1971.
I. J. Schoenberg,On best approximation of linear operators, Indag. Math.26 (1964), 155–163.
I. J. Schoenberg,Monosplines and quadrature formulae, in: Theory and applications of spline functions, T. N. E. Greville (Editor), Academic Press, New York, 1969, pp. 157–207.
I. J. Schoenberg,Cardinal interpolation and spline functions, J. Approximation Theory2 (1969), 167–206. Also MRC Tech. Sum. Rep. #852.
I. J. Schoenberg,Cardinal interpolation and spline functions. II.The case of data of power growth, J. Approximation Theory6 (1972), 404–420. Also MRC Tech. Sum. Rep. #1104.
I. J. Schoenberg,Cardinal interpolation and spline functions IV.The exponential Euler splines, in: Linear Operators and Approximation (Proc. of Oberwolfach Conference, August 14–22, 1971). ISNM20 (1972), 382–404. Also MRC Tech. Sum. Rep. #1153.
I. S. Schoenberg and A. Sharma,Cardinal interpolation and spline functions V.The B-spline for cardinal Hermite interpolation, J. Linear Algebra Appl.7 (1973), 1–42. Also MRC Tech. Sum. Rep. #1150.
I. J. Schoenberg,On cubic spline interpolation at equidistant nodes, MRC Tech. Sum. Rep. #1121.
I. J. Schoenberg,On equidistant cubic spline interpolation, Bull. Amer. Math. Soc.77 (1971), 1039–1044.
I. J. Schoenberg and A. Sharma,The interpolatory background of the Euler-Maclaurin quadrature formula, Bull. Amer. Math. Soc.77 (1971), 1034–1038.
I. J. Schoenberg,On monosplines of least square deviation and best quadrature formulae II, J. SIAM Numer. Anal.3 (1966), 321–328.
I. J. Schoenberg, and S. D. Silliman,In semi-cardinal quadrature formulae, MRC Tech. Sum. Rep. #1300. To appear in the April 1974 issue of Math. Comp.
S. D. Silliman,The numerical evaluation by splines of the Fourier transform and the Laplace transform, University of Wisconsin Ph. D. thesis, August 1971.
Author information
Authors and Affiliations
Additional information
Sponsored by U.S. Army under Contract No. DA-31-124-ARO-D-462.
Rights and permissions
About this article
Cite this article
Schoenberg, I.J. Cardinal interpolation and spline functions VI. Semi-cardinal interpolation and quadrature formulae. J. Anal. Math. 27, 159–204 (1974). https://doi.org/10.1007/BF02788646
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02788646