WOLFRAM

InterpolatingFunction[domain,table]

represents an approximate function whose values are found by interpolation.

Details

Examples

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Basic Examples  (2)Summary of the most common use cases

Make an InterpolatingFunction object that will go through the given points:

Only the domain is shown in standard output format:

Out[2]=2

Evaluate the function at a point in the domain:

Out[3]=3

Plot the function over its domain, showing the interpolation points:

Out[4]=4

Get an InterpolatingFunction object approximating the solution of a differential equation:

Out[1]=1

Plot the function and its derivative:

Out[2]=2

Find the indefinite integral of the solution:

Out[3]=3
Out[4]=4

Scope  (5)Survey of the scope of standard use cases

Make an InterpolatingFunction with exact data:

Out[1]=1

Compute the value using exact arithmetic:

Out[2]=2

Compute using machine-number arithmetic:

Out[3]=3

Compute using arbitrary-precision arithmetic:

Out[4]=4

Make a new InterpolatingFunction with numerical values of all the data:

Out[5]=5

With this InterpolatingFunction values are computed using machine arithmetic:

Out[6]=6

Integrate an InterpolatingFunction:

Out[2]=2

Make a new InterpolatingFunction that is the indefinite integral:

Out[3]=3
Out[4]=4

The derivative of an InterpolatingFunction is another InterpolatingFunction:

Out[2]=2
Out[3]=3

Use partial derivatives of an InterpolatingFunction to check the residual for a PDE:

Out[2]=2

Make an InterpolatingFunction that takes 4 arguments:

Out[1]=1

Integrate it across the first and last dimensions:

Out[2]=2
Out[3]=3

Properties & Relations  (1)Properties of the function, and connections to other functions

InterpolatingFunction does a Piecewise polynomial interpolation:

Out[1]=1
Out[2]=2
Out[3]=3
Wolfram Research (1991), InterpolatingFunction, Wolfram Language function, https://reference.wolfram.com/language/ref/InterpolatingFunction.html (updated 1996).
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).

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.

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

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: 21-January-2025 ]}

@misc{reference.wolfram_2024_interpolatingfunction, author="Wolfram Research", title="{InterpolatingFunction}", year="1996", howpublished="\url{https://reference.wolfram.com/language/ref/InterpolatingFunction.html}", note=[Accessed: 21-January-2025 ]}

BibLaTeX

@online{reference.wolfram_2024_interpolatingfunction, organization={Wolfram Research}, title={InterpolatingFunction}, year={1996}, url={https://reference.wolfram.com/language/ref/InterpolatingFunction.html}, note=[Accessed: 21-January-2025 ]}

@online{reference.wolfram_2024_interpolatingfunction, organization={Wolfram Research}, title={InterpolatingFunction}, year={1996}, url={https://reference.wolfram.com/language/ref/InterpolatingFunction.html}, note=[Accessed: 21-January-2025 ]}