Lagrange Interpolation Visualization

Lagrange interpolation is a method for finding a polynomial that passes through a given set of points. This interactive visualization demonstrates how the Lagrange interpolating polynomial is constructed using basis polynomials and how it perfectly fits through all the given data points.

Mathematical Background

Given $n+1$ distinct points $(x_0, y_0), (x_1, y_1), \ldots, (x_n, y_n)$, the Lagrange interpolating polynomial $P(x)$ is defined as:

$P(x) = \sum_{i=0}^{n} y_i \cdot L_i(x)$

Where $L_i(x)$ are the Lagrange basis polynomials:

$L_i(x) = \prod_{\substack{j=0 \\ j \neq i}}^{n} \frac{x - x_j}{x_i - x_j}$