Commun. Korean Math. Soc. 2008 Vol. 23, No. 2, 295-305 Printed June 1, 2008
Kyung Joong Kim Korea Aerospace University
Abstract : This paper demonstrates how composite-exponential-fitting interpolation rules can be constructed to fit an oscillatory function using not only pointwise values of that function but also of that functions's derivative on a closed and bounded interval of interest. This is done in the framework of exponential-fitting techniques. These rules extend the classical composite cubic Hermite interpolating polynomials in the sense that they become the classical composite polynomials as a parameter tends to zero. Some examples are provided to compare the newly constructed rules with the classical composite cubic Hermite interpolating polynomials (or recently developed interpolation rules).