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:
“Capital is a result of labor, and is used by labor to assist it in further production. Labor is the active and initial force, and labor is therefore the employer of capital.”
—Henry George (1839–1897)
“Any relation to the land, the habit of tilling it, or mining it, or even hunting on it, generates the feeling of patriotism. He who keeps shop on it, or he who merely uses it as a support to his desk and ledger, or to his manufactory, values it less.”
—Ralph Waldo Emerson (1803–1882)