ABSTRACT In 2021, Böttcher, Gasca, Grudsky, and Kozak showed that the limit set of the spectra of tetradiagonal Toeplitz matrices consists of one, two, or three analytic arcs in the complex plane. Building on this result, in two recent papers, the authors constructed and rigorously justified a uniform asymptotic expansion for all eigenvalues in the case where the limit set is a single arc. In the present work, we take the next natural step in addressing the asymptotic approximation of the corresponding eigenvectors in this single‐arc setting. The resulting formulas explicitly reveal the structure of the eigenvectors. We also provide numerical examples that illustrate the high accuracy and linear‐time computability of the proposed approximations.
Bogoya et al. (Mon,) studied this question.