n this section we document a negative
result. We make a natural attempt to switch to a symmetrical problem and find
that such transformation does not bring noticeable benefit.
We start from the
of the section (
) and multiply it with the operator
We obtain a system with symmetrical
We aim for the matrixes
to be as small as possible. The symmetrization step took us in opposite
We note that we cannot apply the diagonal preconditioner of the section
because such operation looses the symmetry. Hence, we attempt the following
for some new diagonal matrix
that we select from minimization of Frobenius norm. We
and we select
We seek the local
We arrived to a system of linear
The symmetry is the only good feature of this system.
The numerical experiment in the script blackDp.py shows that the condition
is 1883. The good thing is we do not need
to be exact. However, given results of the non-symmetric line of calculation,
this is not worth pursuing further.