Asymptotics of eigenvalues of symmetric Toeplitz band matrices

In this paper we obtain uniform asymptotic formulas for all eigenvalues of symmetric Toeplitz band matrices of large dimension. The entries of the matrices are assumed to be complex, that is, the matrices need not necessarily be self-adjoint. The formulas presented allow a detailed study of the structure of the eigenvalues and of their location in the complex plane, and to build an efficient algorithm for finding their numerical values for matrices of medium and high dimension.