Interpolation of a data set by a Newton's divided differences interpolation polynomial.

Usage: Create a data set file with the data to interpolate and call the Interpolate procedure with the filename as argument. A polynomial is returned at the form:

X^N + X^(N-1) + ... + X + c

and a accuracy test is done to verify the accuracy of the generated polynomial. The accuracy is defined in the range 0.0 .. 1.0.

Data set format:

The data set file contain two column one for the X values and one for the F(X) values:

X F(X) 1.0 1.0 2.0 4.0 3.0 9.0 4.0 16.0

Remember to end the data files with a blank line.