Among options for NIntegrate one finds the following construction Method->{name1, Method->name2}. For example, Method -> {"EvenOddSubdivision", Method -> "LocalAdaptive"}. It seems that both "EvenOddSubdivision" and "LocalAdaptive" can be used as the integration methods. Then the question arises, what does their combination mean?

I failed to find an explanation what means the second Method here.

I would like to understand, how to find out, what methods could be combined together this way. For example, can one combine like Method -> {"EvenOddSubdivision", Method -> "AdaptiveMonteCarlo"}?


closed as off-topic by m_goldberg, José Antonio Díaz Navas, LCarvalho, MarcoB, J. M. will be back soon Mar 4 '18 at 20:47

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    $\begingroup$ As far as i can tell, the second Method is a submethod of the first. If Mathematica really accepts these settings (and does really different things) then this means that you can have "EvenOddSubdivision" with "LocalAdaptive" and "AdaptiveMonteCarlo" as strategies for subdivision. Other methods than ``"EvenOddSubdivision"` might not support the same subobtions. At least that is how it works for the Methods of LinearSolve, FindRoot, and FindMinimum with which I am more familiar. However, I cannot tell what the precise meaning of these combinations is. $\endgroup$ – Henrik Schumacher Feb 25 '18 at 11:31
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    $\begingroup$ Some of this is explained in the tutorial "Advanced Numerical Integration in the Wolfram Language". See tutorial/NIntegrateOverview in the Documentation Center. $\endgroup$ – Daniel Lichtblau Feb 25 '18 at 16:19
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    $\begingroup$ There's Method -> { strategy, Method -> rule } and some strategies, can be nested such as preprocessors like "EvenOddSubdivision": Method -> {"EvenOddSubdivision", Method -> {"LocalAdaptive", Method -> {"ClenshawCurtisRule"}}}. $\endgroup$ – Michael E2 Feb 25 '18 at 18:19