Given rank $r$ $A\in\Bbb R^{n\times m}$, is there a procedure to find $XY=A$ such that $X\in\Bbb R^{n\times r}$, $Y\in\Bbb R^{r\times m}$ with property that $\max_{i,j}|x_{i,j}|$, $\max_{i,j}|y_{i,j}|$ is minimized? Is there a suitable software?
If additionally $X=Y',m=n$ could we always have a procedure to factorization?