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.

Scale:

Lagrange:

Points:

Load from file:

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 x_{1}, y_{1}, x_{2}, y_{2}, ...

The individual Lagrange polynomials are:

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

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