> 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 >
