Hi,


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.)


Thanks!



Recommendations for sparse iterative solvers to find a matrix inverse 
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.


The short answer is: don't do it. :)


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.


