Given a fixed $m\times n$ matrix $A$ over reals, which $n\times m$ real-valued matrices $B$ guarantee that $BA$ is stable, ie all eigenvalues have negative real part?
Motivation: any such matrix should correspond to a convergent iterative method for solving a consistent system of linear equations $Ax=b$: pick small-enough $\mu>0$ and arbitrary $x$ and iterate $x = x+\mu B(Ax-b)$ until convergence.
- $B=-A^\dagger$ gives Newton's method
- $B=-A^T$ is batched LMS
- $B=-I$ is Richardson iteration (convergent when $A\succ 0$)