On Thu, Nov 26, 2009 at 2:09 PM, Marco Caliari
<address@hidden> wrote:
On Thu, 26 Nov 2009, Jaroslav Hajek wrote:
On Thu, Nov 26, 2009 at 12:19 PM, Marco Caliari <address@hidden>wrote:
Dear maintainers,
I have seen changeset
http://hg.savannah.gnu.org/hgweb/octave/rev/87595d714005 about normest, by
Jaroslav. As already discussed, the choice
x = norm (A, "columns").'
for the initial vector leads to wrong values (second largest eigenvalue)
for some "important" matrices, like
toeplitz([-2,1,zeros(1,2)]), toeplitz([-2,1,zeros(1,4)]), etc
This was the reason for the old random initial vector. I agree it is not
nice to have slightly different results at each run, but it is not nice to
have wrong values, too.
Best regards,
Marco
Already discussed? When? I couldn't find anything.
http://www-old.cae.wisc.edu/pipermail/octave-maintainers/2006-December/001422.html
I see, thanks. I randomized the guess again. My problem with the previous code was that a priori forming A'*A is quite costly, especially if you want just low precision and expect just a dozen iterations:
A = rand (1e3);
tic; [e,c] = normest (A); toc
tic; [e,c] = normest (A, 1e-1); toc
now:
Elapsed time is 0.0229969 seconds.
Elapsed time is 0.0183249 seconds.
previously:
Elapsed time is 0.220653 seconds.
Elapsed time is 0.210241 seconds.
It's no problem to randomize it again, but I think a non-random behavior is
preferable.
I agree.
Maybe there could be an option to specify the initial vector?
Can the initial vector be improved somehow?
I have no idea. It is usually written "take the initial vector you want: roundoff errors will do the rest".