Lagrange Interpolating Polynomial

Lagrange polynomials are computed using the formula :

$$$ P(X)=\sum_{j=0}^n y_j \left(\prod_{i=0,i\neq j}^n \frac{X-x_i}{x_j-x_i} \right) $$$

with the dots \( (x_0, y_0),\dots,(x_n, y_n) \) and \( x_i \) distinct.

From the points whose coordinates are known, the lagrange polynomial calculator can thus predict other points based on the assumption that the curve formed by these points is derived from a polynomial equation.

dCode allow to use the Lagrangian method for interpolating a Polynomial and finds back the original equation using known points (x,y) values.

Example: By the knowledgeof the points \( (x,y) \) : \( (0,0),(2,4),(4,16) \) the Polynomial Lagrangian Interpolation method allow to find back the équation \( y = x^2 \). Once deducted, the interpolating function \( f(x) = x^2 \) allow to estimate the value for \( x = 3 \), here \( f(x) = 9 \).

The Lagrange interpolation method allows a good approximation of polynomial functions.

There are others interpolation formulas (rather than Lagrange/Rechner) such as Neville interpolation also available online on dCode.

Since the complexity of the calculations increases with the number of points, the program is limited to 25 coordinates (with distinct x-values in the rational number set Q).