Re: Minimizing matrix norm

In fact, I also tried something else: instead of using the Frobenius
norm, I used the [square root of] the sum of the squares of the
OFF-DIAGONAL elements.

This isn't a norm, of course, but it is still easily minimized. My
rationale was sort of a Gershgorin approach: since the spectrum is
contained in a union of disks centered at the diagonal elements, this
tends to concentrate the spectrum near the diagonal.

For my immediate problem, it USUALLY (about 97% of the time) resulted
in a smaller value than the Frobenius value (which is good, from my
point of view). But it was only about 10% less, which wasn't enough of
a reduction to make it worthwhile.

Is anybody familiar with other applications of this idea? Minimizing
the off-diagonal contributions?

--
Ron Bruck



In article <030720061317371148%bruck@xxxxxxxxxxxx>, Ronald Bruck
<bruck@xxxxxxxxxxxx> wrote:

Yes, I've done this too. In fact, since my matrices have integer
entries, the solutions are rational (as is the square of the Frobenius
norm), and I implemented a solver in exact rational arithmetic (using
the Gnu Multi-Precision software package).

But the bounds I get are just too loose, so I'm trying the [much
harder] operator norm.

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