| bitten by Romberg integration [message #7193] |
Thu, 03 October 1996 00:00 |
Mark Fardal
Messages: 51
Registered: October 1995
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Member |
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Hi,
I've been doing an integration with the IDL routine QROMO, which is
an open Romberg algorithm based on the Numerical Recipes routine of
the same name. I called it with eps=1.e-7 to ensure smooth behavior.
However, as I gradually changed the parameters affecting the integrand,
I found the result jumped abruptly by a factor of 1.002. In other
words, the routine underestimated the error by a factor of 2e4.
I've always liked Romberg integration just because it is often so
fast. But I've found similar problems on occasion with the Numerical
Recipes Fortran routine. The problem seemed to be that the routine
will occasionally get a lucky guess as to the answer, and return
prematurely. In the IDL routine I tried setting K=8 instead of K=5
and so far have not have a problem (haven't tested much yet though!)
I've also tried to fix this in the past by requiring two successive
good guesses. But does anyone have another suggestion?
Mark Fardal
University of Colorado
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