This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.

# InterpolatingFunction

 InterpolatingFunctionrepresents an approximate function whose values are found by interpolation.
• In standard output format, only the domain element of an InterpolatingFunction object is printed explicitly. The remaining elements are indicated by . »
• If you supply arguments outside of the domain, a warning is generated, and then an extrapolated value is returned.
Make an InterpolatingFunction object that will go through the given points:
Only the domain is shown in standard output format:
Evaluate the function at a point in the domain:
Plot the function over its domain, showing the interpolation points:
Get an InterpolatingFunction object approximating the solution of a differential equation:
Plot the function and its derivative:
Find the indefinite integral of the solution:
Make an InterpolatingFunction object that will go through the given points:
Only the domain is shown in standard output format:
 Out[2]=
Evaluate the function at a point in the domain:
 Out[3]=
Plot the function over its domain, showing the interpolation points:
 Out[4]=

Get an InterpolatingFunction object approximating the solution of a differential equation:
 Out[1]=
Plot the function and its derivative:
 Out[2]=
Find the indefinite integral of the solution:
 Out[3]=
 Out[4]=
 Scope   (5)
Make an InterpolatingFunction with exact data:
Compute the value using exact arithmetic:
Compute using machine-number arithmetic:
Compute using arbitrary-precision arithmetic:
Make a new InterpolatingFunction with numerical values of all the data:
With this InterpolatingFunction values are computed using machine arithmetic:
Integrate an InterpolatingFunction:
Make a new InterpolatingFunction that is the indefinite integral:
The derivative of an InterpolatingFunction is another InterpolatingFunction:
Use partial derivatives of an InterpolatingFunction to check the residual for a PDE:
Make an InterpolatingFunction that takes 4 arguments:
Integrate it across the first and last dimensions:
InterpolatingFunction does a Piecewise polynomial interpolation: