I have an inverse problem:
$$ \mathbf{d} = A \mathbf{m} $$
that is under-constrained (e.g. $A \in \mathbb{R}^{3\times 5}$).
One might choose the left pseudoinvers $A^T\left(A^TA\right)^{-1}$ as a model estimate given data $\mathbf{d}$, but this is a poor estimate if the model parameters have very different magnitudes.
If I a rough estimate of the relative size of each model parameter (e.g. $m_1 \approx 10^3\times m_2 \approx -10^2 \times m_3$), how do I apply this information when choosing my model estimator? What sort of vocab/terminology should I look into surrounding this idea?