[SciPy-dev] LAPACK 3.2

[Nils Wagner]

FWIW

  Nils

-------- Original Message --------
Date: Wed, 19 Nov 2008 06:03:40 -0800
From: James Demmel <demmel at cs.berkeley.edu>
To: Kreinovich, Vladik <vladik at utep.edu>, reliable 
computing 
<owner-reliable_computing at interval.louisiana.edu>
CC: James Demmel <demmel at cs.berkeley.edu>
Subject: Announcement for Reliable Computing

I would appreciate it if you could post this on your 
mailing list.
Thanks,
Jim Demmel

Subject: New LAPACK release with "guaranteed" error bounds

We have just released LAPACK 3.2, which among other 
improvements
includes iterative refinement for solving linear systems 
with
"guaranteed" error bounds, measured both normwise and 
componentwise.
Portable high precision arithmetic (using another package 
we just
released called XBLAS) is used to compute residuals. What 
we mean
by "guarantee" is that either the error bound is correctly
O(machine_epsilon), or a warning is returned that the 
condition number
is ~1/machine_epsilon or larger. In extensive testing, we 
have never
found it
to fail, either by returning a too-small error bound, or 
failing to solve
a problem whose condition number is at least a little 
below
1/machine_epsilon.

But if there is a community that can find a failure, it is 
this one, and we
would be very interested if you can find one. Since we are 
not doing
interval arithmetic, we expect to keep "guaranteed" in 
quotation marks.

For more information, please see
    http://www.netlib.org/lapack/ and 
http://www.netlib.org/xblas/
    http://www.netlib.org/lapack/lapack-3.2.html

Regards,
Jim Demmel, and the rest of the LAPACK team