# InterpolatingFunction

InterpolatingFunction[domain,table]

represents an approximate function whose values are found by interpolation.

# 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:

Wolfram Research (1991), InterpolatingFunction, Wolfram Language function, https://reference.wolfram.com/language/ref/InterpolatingFunction.html (updated 1996).

#### Text

Wolfram Research (1991), InterpolatingFunction, Wolfram Language function, https://reference.wolfram.com/language/ref/InterpolatingFunction.html (updated 1996).

#### CMS

Wolfram Language. 1991. "InterpolatingFunction." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 1996. https://reference.wolfram.com/language/ref/InterpolatingFunction.html.

#### APA

Wolfram Language. (1991). InterpolatingFunction. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/InterpolatingFunction.html

#### BibTeX

@misc{reference.wolfram_2024_interpolatingfunction, author="Wolfram Research", title="{InterpolatingFunction}", year="1996", howpublished="\url{https://reference.wolfram.com/language/ref/InterpolatingFunction.html}", note=[Accessed: 24-June-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2024_interpolatingfunction, organization={Wolfram Research}, title={InterpolatingFunction}, year={1996}, url={https://reference.wolfram.com/language/ref/InterpolatingFunction.html}, note=[Accessed: 24-June-2024 ]}