most recent 30 from http://mathoverflow.net 2013-06-18T06:53:47Z http://mathoverflow.net/feeds/question/98420 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/98420/recommendations-for-sparse-iterative-solvers-to-find-a-matrix-inverse Nicholas Andrews 2012-05-30T21:43:25Z 2012-05-30T21:52:19Z

<p>Hi,</p> <p>All iterative solvers I've been able to find are for a system Ax = b where b is a vector. Does anyone know of general iterative solvers for AX = B where X, B are matrices, or more specifically finding the inverse A^-1? (Assuming A is large and sparse.)</p> <p>Thanks!</p>

http://mathoverflow.net/questions/98420/recommendations-for-sparse-iterative-solvers-to-find-a-matrix-inverse/98422#98422 Federico Poloni 2012-05-30T21:52:19Z 2012-05-30T21:52:19Z

<p>Unless your matrices have a special structure, both $A^{-1}$ and $A^{-1}B$ are dense (full), general matrices without any special properties. Even storing them in memory will be prohibitive.</p> <p>The short answer is: don't do it. :)</p> <p>The long answer is: look for structure in your matrices, and exploit it. If there is no structure and you really need to perform this computation, then your best bet is using an exact solver, not an iterative one. It will be extremely slow ($O(N^3)$ time and $O(N^2)$ storage), but there are no shortcuts.</p>