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Ill Conditioned Linear Systems - zgelsd is worst than zgesv?



We need to solve a ill conditioned linear system of complex numbers.

Using zgesvxx we are able to solve systemd with condition number rcond up to 10^-16 or also 10^-17.
For more crictical cases (rcond lower than 10^-17) we tried to use zgelsd (based on an optimization algorithm), 
but it seems zgelsd is less performing than zgesvxx. 

In other words zgesvxx is able to solve ill conditioned systems that zgelsd is not able to solve and this is a surprise for us. 

Where are we wrong? Any suggestion?



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