Curve Fitting
The problem with the methods described above is that errors will accumulate and the series will tend to diverge from the true function. A solution which guarantees a constant maximum error is to use curve fitting. A minimum of N values are calculated evenly spaced along the range of the desired calculations. Using a curve fitting technique like Gaussian reduction an N-1th degree polynomial interpolation of the function is found. With the optimized polynomial, the initial values can be calculated as above.
Read more about this topic: Difference Engine, Initial Values
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