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I'm using ParallelTable to evaluate a function that involves NIntegrate. There are a lot of NIntegrate::slwcon warning messages. In fact, every kernel prints the same messages.

I am aware that Mathematica is printing these warnings and now want to suppress them. I tried Quiet[] and Off[NIntegrate::slwcon. But they seem to have no effect whatsoever when using ParallelTable.

How can I turn off (any) warning message when using ParallelTable?

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Not knowing quite what you're doing this may or may not help. I think the problem is you're turning the warnings off in the master kernel and the warnings you're seeing come from the slaves. I'd suggest...

ParallelTable[Quiet[your code here],{your iterator here}];

OR

ParallelEvaluate[Off[NIntegrate::slwcon]]; ParallelTable[your code here, {your iterator here}]
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    $\begingroup$ Actually instead of the second option you can just do ParallelTable[Off[NIntegrate::slwcon];your code here,{your iterator here}];. The Off[] call shouldn't take much time, so I think it's safe enough to execute it for each iteration. $\endgroup$ – Ruslan May 3 '15 at 9:15

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