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Re: svds test failure


From: Ed Meyer
Subject: Re: svds test failure
Date: Tue, 31 Jul 2012 13:23:04 -0700



On Tue, Jul 31, 2012 at 12:31 PM, Daniel J Sebald <address@hidden> wrote:
On 07/31/2012 02:22 PM, Ed Meyer wrote:

As I pointed out in the "make check" thread the problem is that we
should not be
using absolute tolerances because that does not account for the size of
the matrix
elements.  What we should do is to estimate if the result lies in the
interval we would
get with roundoff perturbations in the matrix.  If it does, that's as
good as can be expected.
Eispack used to do something like that with their "performance index"
but I think you can
get better estimates.

Give us an idea of what code you are suggesting Ed.  Something like

eps*size(s,1)*size(s,2)

?  Something concerning the rank of the input matrix?

Dan

PS: Did you mean to CC to the maintainers list?

oops - I did mean to CC
I'm attaching a page from a manual I wrote describing how I judge results.  It's more
involved than the old eispack tests and maybe more work than we want to do.
Much simpler would be to just use the norm of the matrix times some factor times
machine epsilon instead of the absolute tolerances.

--
Ed Meyer

Attachment: sens.pdf
Description: Adobe PDF document


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