POLYNOMIAL-FITTING INTERPOLATION RULES GENERATED BY A LINEAR FUNCTIONAL Kim Kyung-Joong;
We construct polynomial-fitting interpolation rules to agree with a function f and its first derivative f` at equally spaced nodes on the interval of interest by introducing a linear functional with which we produce systems of linear equations. We also introduce a matrix whose determinant is not zero. Such a property makes it possible to solve the linear systems and then leads to a conclusion that the rules are uniquely determined for the nodes. An example is investigated to compare the rules with Hermite interpolating polynomials.