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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

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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.

Answers to Questions

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 équationhref \( y = x^2 \)

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 Nevillehref 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).

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