I wrote, concerning the MEDFIT procedure in NR:
> The upshot of that exchange was that I became convinced that that
> author never understood the faulty mathematical foundation of the
> algorithm, even after four careful explanations.
and Pierre Hugonnet asked:
! Do you mean that NR books may be harmful?
I find the NR books to be somewhat paradoxical. They provide what
superficially appears to be a useful and clear introduction to numerical
methods for scientists and engineers who are not experts therein, but
they contain fundamental mistakes that a naive user is unlikely to
notice, perhaps even after getting incorrect answers.
The problem is that the authors have stumbled upon an incorrect
methods problems that had already been solved correctly. A particularly
unfortunate example is the MEDFIT procedure. I refer interested readers
to the description at http://math.jpl.nasa.gov/nr/nr.medfit.html.
Notwithstanding that I forwarded this description to one of the authors,
and tried to explain it thrice more from different viewpoints, the author
insisted there was no problem with MEDFIT. The author's refusal or
inability to understand this problem brings other areas that I have
not studied into question. If the author had admitted the existence
of the problem, and perhaps taken my suggestion to replace MEDFIT with
the (rather old) ACM TOMS algorithm CL1, it would have increased my
confidence that the authors are able and willing to correct the defects,
as they are brought to their attention.
The problem in the MEDFIT case is an arcane one: The procedure depends
on evaluating derivatives at points where they don't exist. Engineers
and scientists are accustomed to working with continuous and continouusly
differentiable functions, so the possibility of the nonexistence of
a derivative, and the possibility that an algorithm may unavoidably
depend on the values of derivatives exactly and only at points where
they do not exist, doesn't occur to them. This is only one example of
a circumstance in which the authors have presented an incorrect method
in a way that is superficially lucid, that is, so that only an expert
would notice that it is faulty. This is the paradox of NR, and the
facet of it that I consider to be a dangerous disservice to the
community of scientists and engineers who are not experts in numerical
computation. In other words, the book is aimed at naive users, but
contains significant fundamental mistakes that only an expert would
notice. Naive users, at whom the books are consciously aimed, are not
in a position to separate the wheat from the chaff.
I have a collection of unsolicited messages concerning NR books and
algorithms at http://math.jpl.nasa.gov/nr. Some of the messages
remark on incorrect mathematical foundations, some remark on faulty
transformation of mathematics into algorithms, some remark on faulty
transformation of algorithms to software, and some remark on obsolete
methods. I have been told that many of the complaints are obsolete,
but have not been told exactly which ones no longer apply.
Best regards,
Van Snyder
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