Discrete Quartic and Quintic Spline Interpolation

Spline functions are essentially piecewise polynomial functions which meet certain smoothness requirement. The different pieces of spline functions of a certain order provide much greater degree of freedoms in comparison to polynomial functions of the same order. The choiceof these degree of freedom in spline functions makes them quite flexible. The spline functions have played very significant role in the development of the theory ofapproximation and Numerical Analysis. Beside being sufficient and smooth approximation, such functions have nice mathematical properties such as (i) the space of spline functions of a given order has a very convenient base, (ii) similar to polynomials, derivatives and anti-derivative of spline functions are easily obtained in finitely many steps, (iii)splines have sign change property, zero property etc.