Newton Divided Difference Interpolation Formula/Table

Newton Divided Difference Interpolation Formula: 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.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): divided difference interpolation formula
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): divided difference interpolation formula