On the general Hermite cardinal interpolation
HTML articles powered by AMS MathViewer
- by R. Kreß PDF
- Math. Comp. 26 (1972), 925-933 Request permission
Abstract:
A sequence of interpolation series is given which generalizes Whittaker’s cardinal function to the case of Hermite interpolation. By integrating the interpolation series, a sequence of new quadrature formulae for $\int _{ - \infty }^\infty {f(x)dx}$ is obtained. Derivative-free remainders are stated for these interpolation and quadrature formulae.References
- E. T. Goodwin, The evaluation of integrals of the form $\int ^\infty _{-\infty } f(x) e^{-x^{2}} dx$, Proc. Cambridge Philos. Soc. 45 (1949), 241–245. MR 29281, DOI 10.1017/s0305004100024786
- Rainer Kress, Interpolation auf einem unendlichen Intervall, Computing (Arch. Elektron. Rechnen) 6 (1970), 274–288 (German, with English summary). MR 298874, DOI 10.1007/bf02238812
- Rainer Kreß, On general Hermite trigonometric interpolation, Numer. Math. 20 (1972/73), 125–138. MR 319347, DOI 10.1007/BF01404402
- Erich Martensen, Zur numerischen Auswertung uneigenlicher Integrale, Z. Angew. Math. Mech. 48 (1968), T83–T85 (German). MR 256565
- John McNamee, Error-bounds for the evaluation of integrals by the Euler-Maclaurin formula and by Gauss-type formulae, Math. Comp. 18 (1964), 368–381. MR 185804, DOI 10.1090/S0025-5718-1964-0185804-1
- J. McNamee, F. Stenger, and E. L. Whitney, Whittaker’s cardinal function in retrospect, Math. Comp. 25 (1971), 141–154. MR 301428, DOI 10.1090/S0025-5718-1971-0301428-0
Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Math. Comp. 26 (1972), 925-933
- MSC: Primary 41A05
- DOI: https://doi.org/10.1090/S0025-5718-1972-0320586-6
- MathSciNet review: 0320586