[petsc-users] SLEPc EPS Tolerance

[Jose E. Roman]

> El 10 jul 2020, a las 12:54, Eda Oktay <eda.oktay at metu.edu.tr> escribió:
> 
>> How do you measure accuracy?
> Using the word accuracy may be not true actually, I am sorry. I am
> using eigenvectors corresponding to these eigenvalues in k-means
> algorithm, then do spectral graph partitioning. I must look at the
> partition quality. By quality, I mean, the resulting edge cut of my
> partitioned graph. I thought that the less tolerance results in more
> accuracy, hence more qualified partition.
> 
>> What do you mean "the result was still the same"?
> I mean I am still not getting the most qualified solution in E-10,
> still E-2 or E-6 gives more qualified partitions, i.e. they give less
> edge cut.
> 
>> What is the eigenvalue you are computing?
> I am computing the smallest eigenvalue of a Laplacian matrix.

You should compute the residual norm, for instance with -eps_error_relative ::ascii_info_detail (see section 2.5.4 of the manual).
The relative residual error should be in the order of the tolerance (or smaller) if using the default convergence test, but if you are computing a zero eigenvalue then you may want to use an absolute convergence criterion (see table 2.6 or the manual). A graph Laplacian has at least one zero eigenvalue, unless you deflate it as explained in section 2.6.2 of the manual, see also ex11.c https://slepc.upv.es/documentation/current/src/eps/tutorials/ex11.c.html

Jose