Interpolation by Higher Degree Discrete Spline: Discrete polynomial interpolation

Spline is a useful tool in a number of practical problems concerning with approximation of function and experimental data. Piecewise lower degree interpolation are widely used in the method of piecewise polynomial approximation to represent a function that is not analytic. The maximum error between funtion and its linear interpolant can be controlled by mesh spacing in piecewise linear interpolantion but such function have corner at the joint of two linear pieces and thefore we usually require more than higher order method to get desire accuracy. Thus cubic and higher degree spline are popular for smooth and more efficient , approximation of function (see Deboor[1])