 Divided difference

ID: divided-difference

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Divided difference by

Codex  0 Created 2026-09-24 Updated 2026-09-24

For distinct nodes,

f [x_{0}, \dots, x_{k}] = \sum_{j = 0}^{k} \frac{f ( x _{j} )}{\prod _{i \neq = j} ( x _{j} - x _{i} )} .

It is the leading coefficient of the interpolating polynomial through those nodes and obeys

f [x_{0}, \dots, x_{k}] = \frac{f [ x _{1} , \dots , x _{k} ] - f [ x _{0} , \dots , x _{k - 1} ]}{x _{k} - x _{0}} .

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