Abstract
We consider an application of iterated cubic splines to the Euler-MacLaurin integration formula. Some numerical examples are given to illustrate the usefulness of our methods.
Zusammenfassung
Wir erarbeiten eine Anwendung iterativer kubischer Splines auf die Euler-MacLaurin-Integrationsformeln. Wir geben einige numerische Beispiele, um den Nutzen unserer Methoden zu illustrieren.
References
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Sakai, M., Usmani, R.: On consistency relations for cubic splines-on-splines and asymptotic error estimates. J. Approx. Theory45, 195–200 (1985).
Sakai, M., Usmani, R.: On spline-on-spline numerical integration formula. J. Approx. Theory59, 350–355 (1989).
Shelley, M., Baker, G.: On order-preserving approximation to successive derivatives of periodic functions by iterated splines. SIAM. J. Numer. Anal.25, 1442–1452 (1988).
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Sakai, M., Usmani, R.A. Numerical integration formulas based on iterated cubic splines. Computing 52, 309–314 (1994). https://doi.org/10.1007/BF02246511
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DOI: https://doi.org/10.1007/BF02246511