PPT Slide
Definition 5.1 (Cubic Spline Interpolant). Suppose that are N+1 points where a = x0 < x1 < … < xN = b. The function S(x) is called a cubic spline if there exists N cubic polynomials Sk(x) with the properties :
I. S(x)=Sk(x)=sk,0+sk,1(x-xk)+sk,2(x - xk)2+sk,3(x - xk)3 for for each k = 0, 1, . . . , N - 1.
II. S(xk) = yk for k = 0, 1, . . . , N.
The spline passes through each data point.