# Lagrange Interpolation Calculator

## Calculator for the calculation of the interpolation polynomial

The calculator calculates the Lagrange polynomials and the interpolation polynomial for any definable points. The points can be entered in tabular form or alternatively loaded from a file.

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Axes ranges

x-min=
x-max=
y-min=
y-max=
Lagrange:
Points:
Number of points =

An alternative input is possible by loading the data from a file. The values must be separated by comma, space or semicolon and must be in pairs x1, y1, x2, y2, ...

### Lagrange Polynom

Lagrange interpolation is a method for determining a polynomial function passing through a given number of points. It allows a function to be estimated using some known values, called grid points. Since Lagrange basis functions are non-zero at only one point and 1 at all other points, the Lagrange polynomial at any given point is equal to the corresponding grid point. The Lagrange interpolation method has its applications in areas such as numerics, mathematical modeling, and signal processing. A disadvantage is that it produces very high degree polynomials very quickly with many grid points.

The individual Lagrange polynomials are:

${L}_{i}\left(x\right)=\frac{\left(x-{x}_{0}\right)\dots \left(x-{x}_{i-1}\right)\left(x-{x}_{i+1}\right)\dots \left(x-{x}_{n}\right)}{\left({x}_{i}-{x}_{0}\right)\dots \left({x}_{i}-{x}_{i-1}\right)\left({x}_{i}-{x}_{i+1}\right)\dots \left({x}_{i}-{x}_{n}\right)}$

The Lagrange interpolation polynomial is:

${I}_{n}\left(x\right)=\sum _{i=0}^{n}{y}_{i}\cdot {L}_{i}\left(x\right)$

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Index Newton Interpolation Horners Method Curve fit Fitting Gaussian distribution Mean Value Calculator Fourier series calculator Taylor-Series