MaxRecursion

MaxRecursion

is an option for functions like NIntegrate and Plot that specifies how many recursive subdivisions can be made.

Details

  • MaxRecursion->n specifies that up to n levels of recursion should be done.
  • Recursive subdivision is done only in those places where more samples seem to be needed in order to achieve results with a certain level of quality.
  • In d dimensions, each recursive subdivision increases the number of samples taken by a factor that increases roughly exponentially with d.
  • MaxRecursion->Infinity specifies no limit on the number of recursive subdivisions.
  • In cases such as functions with discontinuities or with infinitely rapid oscillations there may be no convergence even after an infinite number of subdivisions.

Examples

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Basic Examples  (2)

Get a very high-quality plot of a sharp feature:

Allow more adaptive recursion to resolve the integral of a rapidly varying function:

Scope  (2)

Use MaxRecursion to control adaptive subdivision:

Use MaxRecursion to improve results when singularities affect numerical integration:

With the default setting, the result is not as good:

Specifying the singularity locations is even more efficient:

Wolfram Research (1991), MaxRecursion, Wolfram Language function, https://reference.wolfram.com/language/ref/MaxRecursion.html (updated 2007).

Text

Wolfram Research (1991), MaxRecursion, Wolfram Language function, https://reference.wolfram.com/language/ref/MaxRecursion.html (updated 2007).

CMS

Wolfram Language. 1991. "MaxRecursion." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2007. https://reference.wolfram.com/language/ref/MaxRecursion.html.

APA

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

BibTeX

@misc{reference.wolfram_2024_maxrecursion, author="Wolfram Research", title="{MaxRecursion}", year="2007", howpublished="\url{https://reference.wolfram.com/language/ref/MaxRecursion.html}", note=[Accessed: 26-December-2024 ]}

BibLaTeX

@online{reference.wolfram_2024_maxrecursion, organization={Wolfram Research}, title={MaxRecursion}, year={2007}, url={https://reference.wolfram.com/language/ref/MaxRecursion.html}, note=[Accessed: 26-December-2024 ]}