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
Famous quotes containing the words initial and/or values:
“No punishment has ever possessed enough power of deterrence to prevent the commission of crimes. On the contrary, whatever the punishment, once a specific crime has appeared for the first time, its reappearance is more likely than its initial emergence could ever have been.”
—Hannah Arendt (1906–1975)
“The values to which the conservative appeals are inevitably caricatured by the individuals designated to put them into practice.”
—Harold Rosenberg (1906–1978)