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Lagrange Interpolating Polynomial

Tool to find the equation of a function. Lagrange Interpolating Polynomial is a method for finding the equation corresponding to a curve having some dots coordinates of it.

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Lagrange Interpolating Polynomial -

Tag(s) : Mathematics

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# Lagrange Interpolating Polynomial

## Lagrange Interpolation Calculator

Tool to find the equation of a function. Lagrange Interpolating Polynomial is a method for finding the equation corresponding to a curve having some dots coordinates of it.

### How to find the equation of a curve using Lagrange?

Lagrange polynomials are computed using the formula :

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

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 interpolation method 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 $$y = x^2$$

Example: Using $$y = x^2$$, interpolate the value for $$x = 3$$, here $$y = 9$$.

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

There are others interpolation methods such as Neville interpolation also avaiable online on dCode.

### What are the limits for Interpolating with Lagrange?

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 set Q).