Mathematica 9 is now available

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.



Any questions about topics on this page? Click here to get an individual response.Buy NowMore Information
THIS IS DOCUMENTATION FOR AN OBSOLETE PRODUCT.