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I have spent some time to compare LMS analytical result from my own method (MPS) and symmedian (Lemoine) point through geometrics, in the case raised by Andrés.

With a low DOP, it is not necessary to iterate the MPS corrector. Nevertheless, I have introduced such a facility, in order to check was is the impact with a DOP of 3.4.

With 3 iterations, the result is converging to 10° 54.06' S,  178° 54.79' E, plus or minus few minute hundredthes. Not very different from the previous one, indeed.

From this given point, the 3 expected LOPs are as follows:

SIRIUS: + 2.6 NM towards 104.1°; CAPELLA: +3.37 NM towards 8.1°; POLLUX: -4.07 NM towards 48.1°

Using a Mercator pattern in an A3 sheet gives the same position for the Symmedian point of the position triangle (its longest side has 32 cm!).

So I am not sure there was a true problem in this particular case, except some difficulty with accuracy. But good geometrical conditions (lower DOP) should be preferable...

By the way, during last days, I have been led to review my "old" analytical calculus about symmedian point, and I found the reason which gave me doubts in some critical cases.

Thank you Herbert, Greg and Andrés for your indirect contribution to correct it !

Best Regards