channelflow.org

This is an old revision of the document!

---

====== Lagrange Interpolating Polynomial ====== The Lagrange Interpolating Polynomial is a simple-to-understand but mathematically clunky way to construct an $N-1$-order polynomial interpolant to a set of $N$ data points $(x_1, y_1), (x_2, y_2), \ldots, (x_N, y_N)$. The best way to see it is by example for a quadratic fit to three data points $(x_1, y_1), (x_2, y_2), (x_3, y_3)$. Let $P(x)$ be \begin{equation*} P(x) = y_1 \frac{(x-x_2)(x-x_3)}{(x_1-x_2)(x_1-x_3)} + y_1 \frac{(x-x_1)(x-x_3)}{(x_2-x_1)(x_2-x_3)} + y_3 \frac{(x-x_1)(x-x_2)}{(x_3-x_1)(x_3-x_1)} \end{equation*} Obviously,