singular matrix
Chetan Jhurani
chetan at ices.utexas.edu
Thu Apr 16 11:34:32 CDT 2009
> From: Yixun Liu
>
> Hi,
> For Ax=b, A is mxn, m>n. I use CG to resolve it and find the solution
> makes no sense. I guess rank(A) < min(m,n). How to resolve this
> singular system? Use SVD?
Only a square matrix can be singular.
If reinterpreting as a least-squares problem, SVD would be slower.
If rank(A) = n, see
<http://en.wikipedia.org/wiki/Moore-Penrose_pseudoinverse#The_QR_method>
If A is dense, use LAPACK for QR, otherwise sparse QR factorization
should be faster. http://www.cise.ufl.edu/research/sparse/CSparse/
If A is not full rank (rank(A) < n), it is more complicated. The
pseudoinverse does not have a simple formula, although it is still
computable for getting the minimum norm solution. The book by Ake
Bjorck would be useful, as Matt already suggested.
Chetan
> Best,
>
> Yixun
>
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