[R] integrate function

[Roger Peng]

I'm curious to see which methods you tried.  I too am looking for a decent
numerical integration routine.

-roger
_______________________________
UCLA Department of Statistics
rpeng at stat.ucla.edu
http://www.stat.ucla.edu/~rpeng

On Thu, 7 Mar 2002, Richard Condit wrote:

> After finding an error in R's integrate function, I spent some time testing 
> various alternative numerical integration routines I took from the 
> Numerical Recipes book by Press et al. Here is a brief summary of what I found.
> 
> As near as I can tell, no method for numerical integration is foolproof. I 
> believe that no matter the method, functions could be invented to defeat 
> it. In particular, as Ole Christensen pointed out, if a function has 
> positive values only in a very narrow range, then numerical routines cannot 
> be guaranteed to find it.
> 
> R's integrate function works better more often than the alternatives I 
> tested. It succeeded with some very tricky functions that foiled the other 
> methods. But it did fail in some circumstances.
> 
> My only advice about the R integrate function would be to point out in 
> documentation that the value returned as "abs error" is not in fact the 
> error. There is no way I found of calculating the deviation between a 
> numerical estimate of an integral and the true integral. Abs error is 
> simply the change in the estimate between the last 2 iterations of the 
> numerical routine. In many cases, this should be a rough approximation of 
> the discrepancy between estimate and true integral, but if integrate fails, 
> abs error fails too. I would suggest abs error not even be returned with 
> the estimate of the integral, since it doesn't add information (since 
> abs.tol is set in the function).
> 
> I can provide more information about the various methods and their errors, 
> if anyone is interested.
> 
> 
> Rick
> 
> 
> 
> -.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-
> r-help mailing list -- Read http://www.ci.tuwien.ac.at/~hornik/R/R-FAQ.html
> Send "info", "help", or "[un]subscribe"
> (in the "body", not the subject !)  To: r-help-request at stat.math.ethz.ch
> _._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._
> 

-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-
r-help mailing list -- Read http://www.ci.tuwien.ac.at/~hornik/R/R-FAQ.html
Send "info", "help", or "[un]subscribe"
(in the "body", not the subject !)  To: r-help-request at stat.math.ethz.ch
_._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._