[petsc-users] SLEPc EPS Tolerance

[Eda Oktay]

No, it is of size 9

Jose E. Roman <jroman at dsic.upv.es>, 10 Tem 2020 Cum, 19:31 tarihinde şunu yazdı:
>
> [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
> >>
>