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- I have used both successfully.
- I used Marquardt's method in the analysis of some
Fermilab
events where on each event, I fitted known shower slopes to measured
photon energy measurements in a segmented lead-scintillator sandwich.
- Here
and the large number of fits 
required a
fast method.
- In these million fits, I saw no problem with divergence.
- This is case where it was necessary to find a fast reliable
method.
- I used the eigenvalue method in analysis of experimental data in
terms of theoretical models.
- Here, one is typically only doing a few (maybe one) fit and so
speed of minimizer is irrelevant.
Geoffrey Fox, Northeast Parallel Architectures Center at Syracuse University, gcf@npac.syr.edu