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", ySpectrum["InterpolationPointsSubdivision",0.2,0.3] gives zero, while ySpectrum["AdaptiveMonteCarlo",0.2,0.3] is non-zero (as it should be, if looking at the initial data). … But how to make "InterpolationPointsSubdivision" work correctly? It does not work properly with non-rectangular regions of integration. …

Now, using "InterpolationPointsSubdivision" and "MaxSubregions: NIntegrate[F02000200L[q],{q,0,1},Method->{"InterpolationPointsSubdivision","MaxSubregions"-> 202,"SymbolicProcessing"-> 0}]//AbsoluteTiming … {23.8689, 0.0670531} NIntegrate[F01200L[q],{q,0,1},Method->{"InterpolationPointsSubdivision","MaxSubregions"->202}]//AbsoluteTiming {0.00181735, 0.0670531} NIntegrate[F011000L[q],{q,0,1},Method->{"InterpolationPointsSubdivision …

Log[k])^2 Log[ 0.41623309053069724` (-4.440892098500626`*^-16 + 0.25` w^2)] Log[ 0.4152917725412687` (2.407945608651872` + Log[k])])), {k, 1, (w^2 - MJpsi^2)/4}, Method -> {"InterpolationPointsSubdivision … ", "MaxSubregions" -> 25000}])) I used method InterpolationPointsSubDivision as suggested in a post by @J.M f52[w_? …

A relatively obvious but poorly documented and probably still not optimal choice for integrands containing interpolating functions is the preprocessor method "InterpolationPointsSubdivision". … Edit: as Alexey has found the improvement in precision is actually independent of the method setting "InterpolationPointsSubdivision", it's rather the combination of "LocalAdaptive", "Partitioning" and …

To do that, I the function Si2[a_, b_] := NIntegrate[Sin[x - y]/(x y), {x, a, b}, {y, x, b}, AccuracyGoal -> 25, PrecisionGoal -> 25, WorkingPrecision -> 40, MaxRecursion -> 1000000, Method -> "InterpolationPointsSubdivision … Note that I use the InterpolationPointsSubdivision method because I saw in various answers that it is a good method to evaluate numerically a highly-oscillatory integrand. …

The way to deal with this is to use the special setting Method -> "InterpolationPointsSubdivision" of NIntegrate[], which will automagically split the integrand so that an integration rule (by default, … "]] // AbsoluteTiming {0.0798281, {-0.00929476, -0.00291246}} Options[NIntegrate`InterpolationPointsSubdivision] displays the suboptions that can be fed to this method. …

Verify how many interpolation points are used in the integration interval of interest: Count[Flatten[derPhi["Grid"]], x_ /; 1/4 < x < 1/2] 63 We can then use the "InterpolationPointsSubdivision" … The count above is well within the default setting of "MaxSubregions", so that doesn't need to be adjusted: NIntegrate[derPhi[x], {x, 1/4, 1/2}, Method -> {"InterpolationPointsSubdivision" …

With this, the PDF is just cdfEmpirical'[x], which we can now use with NIntegrate[] NIntegrate[x cdfEmpirical'[x], {x, 0, xdat[[-1]]}, Method -> "InterpolationPointsSubdivision"] 1.99802 … where the preprocessor method "InterpolationPointsSubdivision" allows NIntegrate[] to split the function internally into sections NIntegrate[] can easily handle. …

This has similar oscillatory characteristics as the OP's and can be integrated (after a couple of minutes) with "InterpolationPointsSubdivision": ifn = NDSolveValue[ {y'[x] + (1/2 + 2 Sin[10 x]) y[ … x] == Exp[-Sin[x/100]^2], y[0] == 10}, y, {x, 0, 500}] ListLinePlot@ifn Length[ifn@"Grid"] (* 34655 *) NIntegrate[ifn[x] Exp[10 I x], {x, 0, 500}, Method -> {"InterpolationPointsSubdivision …

weak singularities, which require dense sampling to get an accurate estimate or require the integration region to be broken up according to the pieces of the piecewise interpolation, which is what the "InterpolationPointsSubdivision … i1 = NIntegrate[ DistrToyInterpolated[thh, Eh], {thh, 0, Pi}, {Eh, 125, 3000}, Method -> {"InterpolationPointsSubdivision", "MaxSubregions" -> 315*3000/5, (* slight overestimate from interpolation …

From here, we can use the sRGB conversion functions from this answer, and then use NIntegrate[] with the setting Method -> "InterpolationPointsSubdivision": (* gamma correction *) sRGBGamma = Function … 12.92 z, z <= 0.0031308}}, 1.055 z^(1/2.4) - 0.055]], Listable]; NIntegrate[Clip[#, {0, 1}]/λ^4, {λ, 385, 700}, Method -> "InterpolationPointsSubdivision …

Yet another way to tell Mathematica to automatically split the integrand before integrating is to use the option setting Method -> "InterpolationPointsSubdivision", like so: With[{T = 1, w = 0.05, num … {x, -T/2, T/2, T/(num - 1)}], InterpolationOrder -> 1]]]; With[{T = 1}, Table[NIntegrate[funINT[t] Exp[-2 π I k t/T]/T, {t, -T/2, T/2}, Method -> "InterpolationPointsSubdivision …

If, after all that, you still want to use NIntegrate[], the right Method setting to use is "InterpolationPointsSubdivision", which will split the InterpolatingFunction[] at its grid points, and integrate … With all these considerations: NIntegrate[(10 x - x^2) dw6[x], {x, 0, 10}, Method -> {"InterpolationPointsSubdivision", "MaxSubregions" -> 3000, …

Update: After identifying and fixing a problem with data, we show that the setting the "MaxSubregions" option of "InterpolationPointsSubdivision" to the number intervals created by the interpolation points … First answer To get a complete "InterpolationPointsSubdivision", a sufficient number of subregions needs to be allowed with the "MaxSubregions" option. …

In V9, this is done only if Method -> "InterpolationPointsSubdivision" is used. … samplePlot[ myIntegrationFunction[interpFunc, 8, Method -> {"InterpolationPointsSubdivision", "MaxSubregions" -> 1}] ] NIntegrate::slwcon: Numerical integration converging too slowly; suspect …