OBTAINING A UNIQUE SPLINE FUNCTION TO INTERPOLATE A POLYNOMIAL WITH LACUNARY DATA VALUES - Pankaj Kumar Tripathi; Kulbhushan Singh (Journal of Mechanics of Continua and Mathematical Sciences, 2025)
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 interpolator 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.