In the case of a graph laplacian, you can regularize the problem by deleting one row/column per connected component of the graph and the corresponding entries of the RHS.
-- Steve Vavasis On Wednesday, September 14, 2016 at 11:27:39 PM UTC-4, James Sharpnack wrote: > > Dear Mladen, > > Was there a resolution to this thread? A simpler related question is that > you have a graph Laplacian for a connected graph. Then you know exactly > what the null space is. Using L \ (b - mean(b)) throws the error > " ArgumentError: matrix has one or more zero pivots" where pinv works but > is slow because it doesn't use the sparsity. > > I need this for a graph structured normal means problem, which is super > important. > > --James > > On Monday, April 27, 2015 at 12:27:14 PM UTC-7, Mladen Kolar wrote: >> >> Dear Dominique, >> >> I am not sure that "incomplete Cholesky decomposition" is standard >> terminology. It is used in John Shawe-Taylor's book on kernel methods for >> pattern analysis. >> >> What it means is the following, instead of using the Cholesky >> decomposition A = R'R where R is upper triangular matrix, one approximates >> A as P'*P where P = R[1:T, :] and T is the rank of approximation. Again, >> the idea is that one does not compute full Cholesky, but greedily >> approximates A. >> >> Thanks, Mladen >> >> On Tuesday, April 21, 2015 at 9:30:54 PM UTC-5, Dominique Orban wrote: >>> >>> What do you mean by "incomplete Cholesky"? Could you explain how that >>> would solve your system? >> >>
