Is the default choice of the algorithm the right one? One can see that sage: A.determinant(algorithm="hessenberg") 16801.7979988558 is quite good...
On Monday, 20 January 2014 18:10:43 UTC, Peter Bruin wrote: > > Would it be proper to autoconvert matrices over RR to RDF in case of the >> default precision, so that the more stable numerical algorithms from RDF >> can be used? I had proposed one such change in #13660 ( >> http://trac.sagemath.org/13660 ) in case of eigenvalue/eigenvector >> computations. >> > > Well, it should also be fixed for a RealField of higher precision. An > easy solution for that is to use PARI, which uses a numerically more stable > algorithm (Gaussian elimination, choosing pivots of maximal absolute value; > I don't know about proven error bounds). Example: > > sage: A._pari_().matdet() > 16801.7979988279 # same as when doing the computation over QQ > > Sage's determinant() already uses PARI over Z/nZ for n less than the > machine word size; it would be trivial to adapt it to work also over the > reals. > > Peter > > -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/groups/opt_out.
