[petsc-users] SLEPc EPS Tolerance

[Jose E. Roman]

[Please respond to the list.]

Is your matrix of size 8? This would explain the residuals.

Jose

> El 10 jul 2020, a las 17:10, Eda Oktay <eda.oktay at metu.edu.tr> escribió:
> 
> I computed residual norm via -eps_error_relative::ascii_info_detail
> for different tolerance numbers (e-4, e-6, e-8, e-10). In each
> tolerance, I got the same table below:
> 
> ---------------------- --------------------
>            k             ||Ax-kx||/||kx||
> ---------------------- --------------------
>        3.000000            6.25528e-16
>        3.000000            7.13774e-16
>        3.438447            2.64362e-16
>        5.000000            4.39333e-16
>        6.000000            1.63943e-16
>        6.000000            2.93737e-16
>        6.000000            3.95997e-16
>        7.561553            3.48664e-16
> ---------------------- --------------------
> 
> I understood that since relative error is E-16 and this table shows
> eigenvalues whose relative error are below the tolerance, I am getting
> the same table but I still couldn't understand although relative
> errors are so small, how am I getting the most qualified partition in
> e-4 tolerance, not e-8. I am not computing zero eigenvalue I believe,
> since I am using EPSSetWhichEigenpairs(eps,EPS_SMALLEST_MAGNITUDE);
> and I am not getting zero eigenvalue.
> 
> Thanks so much for answering!
> 
> Jose E. Roman <jroman at dsic.upv.es>, 10 Tem 2020 Cum, 14:09 tarihinde şunu yazdı:
>> 
>> 
>> 
>>> 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
>>