• Interpolation[data] constructs an InterpolatingFunction object that represents an approximation to the data.

• The data can have the forms {{, }, {, }, ... } or {, , ... }, where in the second case, the are taken to have values 1, 2, ... . • Data can be given in the form {{, {, , , ... }}, ... } to specify derivatives as well as values of the function at the points . You can specify different numbers of derivatives at different points. • Function values and derivatives may be real or complex numbers, or arbitrary symbolic expressions. The must be real numbers. • Multidimensional data can be given in the form {{, , ... , }, ... }. Derivatives in this case can be given by replacing and so on by {, {, , ... }}. • Interpolation works by fitting polynomial curves between successive data points. • Interpolation[data] generates an InterpolatingFunction object that returns values with the same precision as those in data. • See also: Fit, ListInterpolation.

Examples

Here are the InstantCalculators for the Interpolation function. Enter the parameters for your calculation and click Calculate to see the result.

Evaluate the function at a point.

You can paste a template for this command via the Text Input button on the Interpolation Function Controller.

Here is a table of values of the square root function at the points 0, 1, 4, ... , 100.

This constructs an approximate function that represents these 11 values on the domain .

The values of the function match the data at the given points.

The function also gives a fair approximation to the square root function at other points between and .

A plot of the difference between the two functions shows that the approximation is better at some points than at others.

Clear the variable definitions.