Answer to Question #94290 in Quantitative Methods for Dorcas

Question

The interpolating polynomial of degree \\(\\leq n\\)with the nodes\\(x_{0}, x_{1},\\cdots, x_{n}\\) can be written as

Answer 1

$p(x) = a_nx^n + a_{n-1}x^{n-1} + \dots + a_2x^2 + a_1x + a_0, \\$

where $p(x_i) = y_i \text{ for all } i \in \{ 0,1,\dots,n \}$.

Lagrange polynomial: $p(x) = \sum_{i=0}^n ( \prod_{0 \leq j \leq n; j \not= i} \frac{x-x_j}{x_i-x_j} ) y_i$

More detailed info: https://en.wikipedia.org/wiki/Polynomial_interpolation