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

open allclose all

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).

BibTeX

@misc{reference.wolfram_2021_maxrecursion, author="Wolfram Research", title="{MaxRecursion}", year="2007", howpublished="\url{https://reference.wolfram.com/language/ref/MaxRecursion.html}", note=[Accessed: 20-October-2021 ]}

BibLaTeX

@online{reference.wolfram_2021_maxrecursion, organization={Wolfram Research}, title={MaxRecursion}, year={2007}, url={https://reference.wolfram.com/language/ref/MaxRecursion.html}, note=[Accessed: 20-October-2021 ]}

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