] represents an approximate function whose values are found by interpolation.
InterpolatingFunction works like Function.
InterpolatingFunction[ ... ][
] finds the value of an approximate function with a particular argument x.
In standard output format, only the domain element of an InterpolatingFunction object is printed explicitly. The remaining elements are indicated by <>.
domain specifies the domain of the data from which the InterpolatingFunction was constructed.
If you supply arguments outside of the domain, a warning is generated, and then an extrapolated value is returned.
InterpolatingFunction objects that take any number of real arguments may be constructed.
You can take derivatives of InterpolatingFunction objects using D and Derivative.
NDSolve returns its results in terms of InterpolatingFunction objects.
See the Mathematica book: Section 1.6.4, Section 2.2.8, Section 3.8.2.
See also Implementation NotesA.9.44.25MainBookLinkOldButtonDataA.9.44.25.
See also: CompiledFunction, FunctionInterpolation.
Related package: NumericalMath`SplineFit`.
Here is a table of values of the reciprocal function and an InterpolatingFunction object that represents the data.
An InterpolatingFunction object can be evaluated just like any other Mathematica function. The approximate function reproduces the values given at the data points and it gives approximate values in between.
The approximate function is close to the original reciprocal function for most values in the domain.
Evaluate the cell to see the graphic.