#12966: Indefinite factorization for exact matrices
----------------------------------+-----------------------------------------
Reporter: rbeezer | Owner: jason, was
Type: enhancement | Status: needs_review
Priority: minor | Milestone: sage-5.1
Component: linear algebra | Resolution:
Keywords: | Work issues:
Report Upstream: N/A | Reviewers:
Authors: Rob Beezer | Merged in:
Dependencies: | Stopgaps:
----------------------------------+-----------------------------------------
Changes (by {'newvalue': u'Rob Beezer', 'oldvalue': ''}):
* status: new => needs_review
* author: => Rob Beezer
Old description:
> Almost any square symmetric (or Hermitian) matrix A over a field can be
> decomposed into a lower triangular matrix L and a diagonal matrix D such
> that A = L*D*L-transpose, suitably adjusted in the Hermitian case.
>
> 1) This is of interest for its own sake (eg for solving systems).
>
> 2) If the field has square roots and the diagonal matrix has positive
> entries, then the Cholesky decomposition is easy. This would fix #11274.
>
> 3) This will give a good way to tell if a matrix is positive definite.
New description:
Almost any square symmetric (or Hermitian) matrix A over a field can be
decomposed into a lower triangular matrix L and a diagonal matrix D such
that A = L*D*L-transpose, suitably adjusted in the Hermitian case.
1) This is of interest for its own sake (eg for solving systems).
2) If the field has square roots and the diagonal matrix has positive
entries, then the Cholesky decomposition is easy. This would fix #11274.
3) This will give a good way to tell if a matrix is positive definite.
'''Apply''':
1. [attachment:trac_12966-indefinite-factorization-v1.patch]
--
Comment:
v1 patch implements general utility function as an underscore method and
then uses this for a user-level method. The utility method will be used
to provide an `is_positive_definite` method and a fixed version of
Cholesky decomposition.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/12966#comment:2>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
--
You received this message because you are subscribed to the Google Groups
"sage-trac" group.
To post to this group, send email to [email protected].
To unsubscribe from this group, send email to
[email protected].
For more options, visit this group at
http://groups.google.com/group/sage-trac?hl=en.
