I was wondering how to solve the following problem (in a least-squares sense):
$$ \mathbf{y}_1 = e^{Ax_1} \mathbf{y}_0 \\ \mathbf{y}_2 = e^{Ax_2} \mathbf{y}_0 \\ \vdots\\ \mathbf{y}_n = e^{Ax_n} \mathbf{y}_0 $$
with vectors $\mathbf{y}_i$ and scalars $x_i$ for $i=0,1,...,n$ all known. In other words; the unknown in this set of equations is the matrix $A$ in the exponential.