Background: I am trying to motivate why I use an SVD instead of an iterative LMS solver for the solution of an equation of the form
$$Ax=b$$
where $A\in\mathbb{C}^{M\times M}$,$x\in\mathbb{C}^{M}$ and $b\in\mathbb{C}^{M}$ and $x$ is unkown. The literature I have read states that a SVD is "numerically robust" (whatever that means) without specifying it further. As far as I understand, the LMS solver also converges to the optimal solution provided by using the SVD but can be slow if the eigenvalue distribution of $A$ is high.
Question: What advantages does the solution of the inverse problem using SVD offer over iterative LMS solvers?