RE: NIntegrate Precision
- To: mathgroup at smc.vnet.net
- Subject: [mg30839] RE: NIntegrate Precision
- From: victork at csse.monash.edu.au (Victor Kowalenko)
- Date: Thu, 20 Sep 2001 03:51:34 -0400 (EDT)
- Organization: The Math Forum
- Sender: owner-wri-mathgroup at wolfram.com
I am interested in obtaining very high precision answers to Mellin-Barnes integrals using at the Compaq Grendel supercomputer at the Victorian Partnership for Advanced Computing in Australia. Typically, I am using NIntegrate to evaluate the contour integrals along the imaginary axis with integrands that are of the following form: (-\exp(i\pi/2)/z)^s \Gamma(s-\nu+1/2) \Gamma(s+\nu +1/2)/(\exp(i\pi s)-\exp(-i\pis)). I create a module that sets s=c+r\exp(i \theta) and invokes the NIntegrate procedure for r ranging from 0 to \infty. MinRecursion and MaxRecursion are set equal to 3 and 10 respectively while WorkingPrecision is set equal to wp. The module calls NINtegrate twice with \theta equal to -\pi/2 and \pi/2 and subtracts the two results. The module is set equal to a function with variables z (typically equal to \exp(49i\pi/100)/2, \nu (initially equal to 1/4), \nu (equal to 1/3, but will become complex) and wp. When wp is set equal to 11, I get a result in FullForm of Complex[-0.051659811688484825`, -1.185784385161031`] For wp=16 I get the same result. However, when I put wp equal to 20 I get Complex[-0.0516598116884759770974000991`10.72885,-1.1857843851610154635167376477`12.0893] I am mystified by what `10.7285 means. In addition the latter value seems to have less precision than the former values although the precision is higher. I would have expected the discrepancy to occur at a high level of precision, although I suspect the last value may be more accurate than the previous two results. Are you able to shed any light on this conundrum?