Matrix-method: compare use of different fixpoints

[bo198214]

Hmm, we are talking about truncated matrices only as approximations, no?
When I compute the eigensystem not by numerical eigensystem-solver for finite matrices (as implemented in a software) but based on an analytical description of each entry, then I actually work with finite truncations of an assumed infinite matrix, which may provide multiple solutions for the same composed theoretical result matrix.

But this is than another method. The matrix operator method is to use truncated Matrices with unique Eigensystem decomposition and hence with a unique limit. That was the absolute good thing about this method as we dont have to take fixed points (with the attached question of which to choose) into consideration.

For the infinite matrices there is not even only one solution for each fixed point but also all the other possible solutions come into play, i.e. the non-regular Schroeder functions. So how should this help? If we know there are some solutions out there which we also want to have and than modify our method (that was designed to be unique) also to include the other solutions???