Spectra and pseudospectra of block Toeplitz matrices

This paper extends previous work by Reichel and Trefethen on the spectra and pseudospectra of Toeplitz matrices to the case of triangular block Toeplitz matrices. In particular, we give results for the pseudospectra of triangular block Toeplitz matrices and operators and show that the pseudospectrum of a triangular block Toeplitz matrix converges to the pseudospectrum of a corresponding triangular block Toeplitz operator. Numerical experiments are presented to demonstrate the variety of pseudospectra that can be exhibited by both triangular and nontriangular block Toeplitz matrices.