OK, I understand your criticisms.

However the question is: are there good alternatives to NR ? A text aimed at non-specialists, correct algorithms (I mean without theoretical mistakes), simple to use routines (I'm aware that simple also often means not the most efficient),... ?


Also, using simple, even not perfectly correct, algorithms is not always a bad idea:

An engineer takes a simple and "false" algorithm (that is also simple to understand) and it works (I mean the results are satifactory for what he wants to do). One day, a case occurs where it fails. Then the engineer tries to understand why it fails in that case. By analysing in which way the problem he tries to solve differs from the previous ones, by reading higher level papers, or asking numerical analysis specialists, he is likely to understand the pitfalls of the algorithm he uses. Then he searches for more sophisticated ones. Now that he understands all the issues of his problem, he can more easily learn and understand them than if he would have gone straigth to them.



However, I agree with you when you say that it's difficult to be confident in NR if the authors do not perfectly understand what they do.



Pierre



Van Snyder wrote:
> 
> 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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