# InterpolatingFunction

InterpolatingFunction[domain,table]

represents an approximate function whose values are found by interpolation.

# Details # Examples

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## Basic Examples(2)

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:

## 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:

## Properties & Relations(1)

InterpolatingFunction does a Piecewise polynomial interpolation: