*To*: mathgroup@smc.vnet.net*Subject*: [mg10597] RE: [mg10481] Method to eliminate*From*: Ersek_Ted%PAX1A@mr.nawcad.navy.mil*Date*: Mon, 26 Jan 1998 04:42:28 -0500

Sean Ross replied to Soo-Hwan: I add some comments below. ---------- |> I want to know the method to eliminate NIntegrate warning. |> |> The two warning message follows : |> |> NIntegrate::slwcon: |> Numerical integration converging too slowly; |> suspect one of the following: singularity, |> oscillatory integrand, or insufficient |> WorkingPrecision. |> |> NIntegrate::ncvb: |> NIntegrate failed to converge to prescribed |> accuracy after 7 recursive bisections in x near |> x = 0.126684. |> |> How can I escape from this problem ? When above-case happened, |> can I believe the accuracy of my data ? | | |A better question is: when you don't get the error message, can you |believe the accuracy of your data? The message is just that, a |warning. If it offends you, turn it off using Off[](see the |mathematica book 2.8.21). Don't blindly trust a numerical routine, |even one as well written as the one in mathematica. Learn about the |issues involved in numeric integrals and write your own routine if you |have any reason to suspect mathematicas. Post your specific problem, and a member of the group might show you how to fix it. Also: Before you write your own algorithm take a look at the various methods that are built in. I have tried to learn how the NIntegrate Options effect the algorithms, and when certain selection are needed. WRI has written some tutorials on this, but not as detailed as I would like. I was able to perform experiments to learn what happens when I use non-default values for GaussPoints, MinRecursion, MaxRecursion, and SingularityDepth. However, it would have been nice if the tutorials illustrated the lessons I had to discover on my own. It would have made it a lot easier (especially since I have no formal education in numerical analysis). To this day I have only a vague understanding of the GaussKronrod method. You might suggest I check a Numerical Analysis book. Well I have checked several, and I have yet to find one that has more than two paragraphs on GaussKronrod integration. The WRI tutorial notes say "Calculating high precision weights and abscissas for the Gauss rule is fairly time consuming for a large number of GaussPoints". OK how about an example to demonstrate this. It's hard to quantify "fairly time consuming". Also I can only make an educated guess at how some other methods work: (DoubleExponential, QuasiMonteCarlo, MultiDimensional, Oscillatory). Some of the Options are not as difficult to understand (AccuracyGoal, WorkingPrecision, Compiled, PrecisionGoal). Perhaps a qualified member of the group would be willing to write a detailed tutorial on the NIntegrate Options. The tutorial could be presented at the Mathematica User Conference, or in the Mathematica Journal. Besides the NIntegrate Options there are likely other the numerical algorithms in Mathematica that could also be discussed. Ted Ersek