OBTAINING A UNIQUE SPLINE FUNCTION TO INTERPOLATE A POLYNOMIAL WITH LACUNARY DATA VALUES

The present paper deals with the problem of obtaining a unique spline function for approximating a polynomial function. We have given values of the polynomial; its first derivatives are at the node points and also the third derivatives are given at the knot points of the unit interval I = [0, 1]. The problem is solved majorly in two parts, the first part shows the unique existence of the interpolatory spline function and the second part deals with the convergence theorem and error bounds. Later we discussed its applications for computer-aided design and image processing also.