NormFunction

NormFunction

is an option for functions such as FindFit and NDSolve which gives a function to be minimized in generating results.

Details

  • NormFunction->f specifies that f[data] should be minimized in generating results.

Examples

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Basic Examples  (2)

Find a "best" fit for data using different norms:

The default is to find the best least-squares fit:

Use the -norm instead:

Use the 1-norm:

Use a 2-norm for estimating local error in solving an ODE:

Use an -norm:

The error measure makes a difference in the solution quality:

Scope  (1)

The norm is used for space and time in PDE solutions:

Plot the actual solution error, when using different error estimation norms:

A plot of the best solution:

Wolfram Research (2003), NormFunction, Wolfram Language function, https://reference.wolfram.com/language/ref/NormFunction.html.

Text

Wolfram Research (2003), NormFunction, Wolfram Language function, https://reference.wolfram.com/language/ref/NormFunction.html.

CMS

Wolfram Language. 2003. "NormFunction." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/NormFunction.html.

APA

Wolfram Language. (2003). NormFunction. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/NormFunction.html

BibTeX

@misc{reference.wolfram_2022_normfunction, author="Wolfram Research", title="{NormFunction}", year="2003", howpublished="\url{https://reference.wolfram.com/language/ref/NormFunction.html}", note=[Accessed: 06-July-2022 ]}

BibLaTeX

@online{reference.wolfram_2022_normfunction, organization={Wolfram Research}, title={NormFunction}, year={2003}, url={https://reference.wolfram.com/language/ref/NormFunction.html}, note=[Accessed: 06-July-2022 ]}