On 10/26/2012 10:01 PM, Jason Grout wrote:
For most computations in Sage, using RR gives better results. The
problem is that no one has implemented numerically stable linear algebra
algorithms for RR/CC/RealField/ComplexField (well, I guess at one point
I had a numerically stable LU decomposition with partial pivoting, but
I'm not sure if that ended up getting committed or not).
Sergey Bochkanov was working on implementing an interface to alglib [1]
to make numerically stable multiprecision linear algebra available:
https://groups.google.com/forum/?fromgroups=#!topic/sage-devel/0sBNEuFCfCs
(search also sage-devel for 'alglib' or posts from Sergey for longer
threads on the subject).
I'd say finishing the interface with alglib (and evaluating the quality
of alglib) would be a very good project for someone to do.
Thanks,
Jason
[1] http://www.alglib.net/
Until that gets in, I put in a patch at #13657 to the tutorial to at
least mention RDF/CDF as the ones to use for eigenvalue and eigenvector
computations. And possible other numerical computations. If you have
anything more to add, then please do so.
http://trac.sagemath.org/13657
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