PPT Slide
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.
III. Sk (xk+1) = Sk+1(xk+1) for k = 0, 1, . . . , N - 2 .
The spline forms a continuous function.
IV. S’k(xk+1) = S’k+1(xk+1) for k = 0, 1, . . . , N - 2.
The spline forms a smooth function.
V. S”k (xk+1) =S”k+1(xk+1) for k = 0, 1, . . . , N - 2.
The second derivative is continuous.