Asymptotics of the smallest singular value of a class of toeplitz–generated matrices and related finite rank perturbations
Abstract
Square matrices of the form Xn = Tn+fn(T
−1
n )
∗
, where Tn is
an n×n invertible banded Toeplitz matrix and fn some positive sequence
are considered. The norms of their inverses are described asymptotically
as their size n increases. Certain finite rank perturbations of these matrices
are shown to have no effect on this behaviour.