Re: Singularity-handling transformation employed by NIntegrate

*To*: mathgroup at smc.vnet.net*Subject*: [mg71191] Re: Singularity-handling transformation employed by NIntegrate*From*: "dimitris" <dimmechan at yahoo.com>*Date*: Fri, 10 Nov 2006 06:37:48 -0500 (EST)*References*: <eiut46$h63$1@smc.vnet.net>

I have searched a lot regarding numerical integration in mathematica. The truth is there are not many sources out there. You can achieve more things with experiment. Even the (giant and amazing book; actually the whole series worth the money!) Mathematica Guidebook for Numerics my M. Trott does not contain much information about SingularityDepth (I hope I don't lose anything!). I copy an except from it... "SingularityDepth is an option for NIntegrate that determines the number of recursive subdivisions of the interval of integration near the endpoints and specified internal points, before a transformation of variables of the endpoints and the specified internal points is to be performed (provided the required accuracy or precision has not yet been achieved)." Another place you might consult is the following link for a presentation of the late Jery B. Keiper at http://library.wolfram.com/infocenter/Conferences/4679/ There is a complete subsection regarding SingularityDepth although it doesn't answer to your question about the transformation. There is also a book called Elementary Numerical Computing with Mathematica (see here for more information http://library.wolfram.com/infocenter/Books/3533/); Maybe you could find some material there; personally, I don't have it. But I think it is out of print. I hope someone else will be more informative; I am also quite interested in the subject. Regards Dimitris Andrew Moylan wrote: > Hi all, > > Further to a previous question: Can anyone tell me what transformation > NIntegrate employs when a singularity is detected (i.e., when the > number of recursive subdivisions specified by SingularityDepth is > reached)? > > Cheers, > Andrew