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

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Newton:

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}, ...

Table for determining the factors α_{i}. These are the red elements in the table. By crossing over them with the mouse, the calculation elements are highlighted.

α_{0} = y_{0}; α_{1} = (y_{1} - y_{0})/(x_{1} - x_{0}); ...

In general, the Newton interpolation polynomial is

p_{n}(x) = α_{0} + α_{1}(x - x_{0}) + α_{2}(x - x_{0})(x - x_{1}) + α_{3}(x - x_{0})(x - x_{1})(x - x_{2}) + ... + α_{n}(x - x_{0})(x - x_{1}) ... (x - x_{n-1})

and with the factors α_{i} from the table and the support values the interpolation polynomial results in

Print or save the image via right mouse click.

Here is a list of further useful sites:

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