Eigenvalues of Non-Hermitian Banded Toeplitz Matrices. Approaching Simple Points of the Limiting Set.

Ponente(s): Sergey Grudskiy Mikhailovich

For large non-Hermitian banded Toeplitz matrices, it is well known that their eigenvalues cluster along a limiting set, which is formed by a finite union of closed analytic arcs. We consider general non-Hermitian banded Toeplitz matrices and extend the simple-loop method to obtain individual asymptotic expansions for eigenvalues approaching simple and non-degenerate points of the limiting set as the matrix order increases to infinity. We also develop an algorithm to effectively compute these expansions.