Interpolation

Lagrange Polynomial Interpolation

Given $n_p$ points $(x_k,y_k),$ the interpolated function values, $f(x)$ are expressed as

$f(x)=\sum_{k=0}^{n} y_{k} L_{k}(x),$

where $L_{k}(x)$ is the Lagrange polynomial given by

$L_{k}(x)=\prod_{\stackrel{i=0}{i\ne k}}^{n}\frac{x-x_{i}}{x_{k}-x_{i}}.$