Eigenvalues of tridiagonal pseudo-Toeplitz matrices (Q1965276)

Eigenvalues are determined for tridiagonal matrices that are not entirely Toeplitz (they contain a Toeplitz matrix in the upper left block). The treatment uses the connection between the characteristic polynomials of these tridiagonal pseudo-Toeplitz matrices and the Chebyshev polynomials of the second kind. The intervals derived from the roots of some Chebyshev polynomial as a reference are used to determine the location of all eigenvalues. For a sequence of tridiagonal matrices with a positive product from each pair of off-diagonal matrices the eigenvalues of two consecutive matrices interlace.