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.

Lagrange Interpolating Polynomial - dCode

Tag(s) : Mathematics

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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.

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.

So using points with known coordinates, it is thus possible to predict other points based on the assumption that the curve formed by these points is derived from a polynomial type equation.

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

Consider the dots \( (0,0),(2,4),(4,16) \), the interpolation allows to get back the equation \( y = x^2 \)

With \( y = x^2 \) you then can interpolate the value for \( x = 3 \), here \( y = 9 \).

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

Calculations' needs can grow rapidly and program is limited to 25 points with distinct x-coordinate in the set Q.

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