Re: unsymmetric eigenvalue problem

[Patrick dot Alken at colorado dot edu]

Thanks for making the test program - its a very good idea! I ran it on a variety
of cases and found that there are some convergence issues in my code. Most of
these can be fixed by increasing UNSYMM_MAX_ITERATIONS in unsymm.c, but on the
other hand I don't think it should be necessary to have so many QR iterations
for convergence.

After a cursory look at LAPACK it seems to me based on a comment in dhseqr that
it reports failure after 30*N total unsuccessful iterations. This seems like a
lot to me, my method reports failure after 30 iterations without finding an
eigenvalue (I don't keep track of total iterations).

Another possibility is the actual algorithm. LAPACK uses the multi-shift QR
algorithm published in 1989, whereas I implemented the original double-shift
algorithm from the 1960s which was described in Golub and Van Loan. I might
look into the multi-shift method when I get some time and see how its
convergence compares with the double-shift method. I'll be away for a week or
so, so I won't have a chance to look at this for a little while.

Thanks,
Patrick Alken