[Bug-gsl] singular Jacobian not detectedby Newton

[Michel Kern]

Hi,
I'm solving small dense (and sometimes nasty) non-linear systems coming 
from chemical equilibrium. Sometimes the solvers fail, but that's life. 
Depending on the system, different methods perform better.
We found a problem with Newton's method: sometimes we encounter a 
singular Jacobian. This is correctly detected by the LU solve routine  
gsl_linalg_LU_solve, but the return code is ignored by newton_iterate 
(line 95 in newton.c).

It would be useful if this routine checked the error status of the 
functions it calls, so the user can do something about it in the calling 
program.
It may require an additional error number, like E_SINGJAC or something 
similar. Is that feasible ?

Anyway, thanks for a very useful piece of software,
Regards,
Blandine Gueslin and Michel Kern

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