ABSTRACT
We will see that this question indeed has a positive answer in some cases, but we will also point out that the posed question is the wrong one in some sense: The point is that the computation of least square solutions is instable with respect to small perturbations. So, even in case we can
A much better question seems to be the following more general one which was perhaps first raised by Moore and Nashed: Is it possible to replace the approximation operators An by certain regularizations, A~ say, which also approximate A, for which the least square solutions of A~xn = Yn converge to the least square solution of Ax = y, and for which this convergence is in some sense stable? We will verify that this problem is equivalent to a generalized invertibllity problem in the c· -algebra :F 1 g and, thus, accessible to algebraic techniques.
