integrate function
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 _._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._
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