Newton Divided Difference Interpolation Formula/Examples
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Examples of Newton Divided Difference Interpolation Formula
Example: $f \sqbrk {0, 1}$
- $f \sqbrk {0, 1} = \dfrac {\map f {x_1} - \map f {x_0} } {x_1 - x_0}$
Table
When manual calculation was the only game in town, it was de rigueur to build the following triangular table of coefficients, to reduce repetitive calculation.
For example, for $n = 3$ the table would have the form:
- $\begin {array} {l|llll} x_0 & f \sqbrk {x_0} & & \\
x_1 & f \sqbrk {x_1} & f \sqbrk {x_0, x_1} & \\ x_2 & f \sqbrk {x_2} & f \sqbrk {x_1, x_2} & f \sqbrk {x_0, x_1, x_2} & & \\ x_3 & f \sqbrk {x_3} & f \sqbrk {x_2, x_3} & f \sqbrk {x_1, x_2, x_3} & f \sqbrk {x_0, x_1, x_2, x_3} & & \\ \end {array}$
to which the computer would calculate each entry from the ones immediately $\gets$ and $\nwarrow$.
This of course can be translated into whatever contemporary software structure is constructed in the software library of your computer language of choice.