Natural cubic spline:If f is defined at x0, x1, ..., xn-1 and h = xi 1 - xi, then f has a unique natural spline interpolation on the nodes xi. The interpolation function S(x) is given by S(x) = ai bi(x - xi) ci(x - xi)^2 di(x - xi)^3 for i = 0, 1, ..., n-1. To obtain the values of bi and di, use the following formulas:bi = (ai 1 - ai) / h - (ci 1 2ci)h / 3di = (ci 1 - ci) / (3h)To solve the equation Ax = h, where A is a tridiagonal matrix, the values of ci can be obtained using the formu
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