Question
Are there libraries out there that implement block Krylov subspace methods? (I was not able to find any from a simple Google search.)
Background
Right now, I am working with a code that solves several systems of the form
\begin{align} Ax_{i} = b_{i}, \end{align}
where $A$ is $n$ by $n$, $i = 1, \ldots, m$, and in general, $n \gg m$ ($n$ is at least 10 times larger than $m$, and could be several orders of magnitude larger than $m$). In addition, $A$ is large enough that iterative methods are preferable.
Currently, the code solves $Ax_{i} = b_{i}$ with a Krylov subspace method for each separate right-hand side with a given preconditioner, and this approach seems to work well enough. (The code also recomputes the preconditioner, which is unnecessary.)
To speed up the code, it seems like it could be worth looking at solving
\begin{align} AX = B \end{align}
instead, where $B = [b_{1}\, b_{2}\, \ldots\, b_{m}]$ is an $n$ by $m$ matrix gathering up all of the $b_{i}$, and $X$ is also an $n$ by $m$ matrix gathering up the $x_{i}$.
I'd like to try out solving $AX = B$ with block Krylov subspace methods (using the same preconditioner as before) to see if it outperforms the current approach of solving $Ax_{i} = b_{i}$ and looping over $i$. It is both possible and unlikely that the solution to $Ax_{i} = b_{i}$ could then be used as a guess for the system $Ax_{j} = b_{j}$ for $i \neq j$; I don't expect there to be a relationship among the various systems.
