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 Numerical calculations Algorithms:  HERMITE INTERPOLATION ALGORITHM

TO OBTAIN THE COEFFICIENTS OF THE HERMITE INTERPOLATING

      POLYNOMIAL H ON THE (N+1) DISTINCT NUMBERS X(0), ..., X(N)
      FOR THE FUNCTION F:

      INPUT:   NUMBERS X(0), X(1), ..., X(N); VALUES F(X(0)), F(X(1)),
               ..., F(X(N)) AND F'(X(0)), F'(X(1)), ..., F'(X(N)).

      OUTPUT:  NUMBERS Q(0,0), Q(1,1), ..., Q(2N + 1,2N + 1) WHERE

               H(X) = Q(0,0) + Q(1,1) * ( X - X(0) ) + Q(2,2) *
                      ( X - X(0) )**2 + Q(3,3) * ( X - X(0) )**2 *
                      ( X - X(1) ) + Q(4,4) * ( X - X(0) )**2 *
                      ( X - X(1) )**2 + ... + Q(2N + 1,2N + 1) *
                      ( X - X(0) )**2 * ( X - X(1) )**2 * ... *
                      ( X - X(N - 1) )**2 * (X - X(N) ).