Initial Values
The initial values of columns can be calculated by first manually calculating N consecutive values of the function and by backtracking, i.e. calculating the required differences.
Col gets the value of the function at the start of computation . Col is the difference between and ...
If the function to be calculated is a polynomial function, expressed as
the initial values can be calculated directly from the constant coefficients a0, a1,a2, ..., an without calculating any data points. The initial values are thus:
- Col = a0
- Col = a1 + a2 + a3 + a4 + ... + an
- Col = 2a2 + 6a3 + 14a4 + 30a5 + ...
- Col = 6a3 + 36a4 + 150a5 + ...
- Col = 24a4 + 240a5 + ...
- Col = 120a5 + ...
Read more about this topic: Difference Engine
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