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Interpolation

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

Using InstantCalculators

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.

Evaluate the function at a point.

Entering Commands Directly

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.