Convergence of Discrete Cubic,Quartic and Quintic Splines: Discrete polynomial Spline Interpolation

Spline function are essential piecewise polynomial function which meet certain smoothness requirement .The different pieces of spline function of certain order provide much greater degree of freedom in compression to polynomial function of same order.The choice of these degree of freedom make them quite flexible .The spline function have played very important role in the development of the theory of approximation and Numerical analysis .Beside being sufficient and smooth approximation such function have nice mathematical properties(i)The space of spline function of certain order have very convenient basis (ii)Similar to polynomial derivative and anti-derivative of spline function are easily obtained in finite many step.