A fast algorithm for computing the pseudospectra of Toeplitz matrices

The concept of pseudospectra was introduced by Trefethen during the 1990s and became a popular tool to explain the behavior of non-normal matrices. In this paper, we propose a fast algorithm for computing the pseudospectra of Toeplitz matrices by using fast Toeplitz QR factorization. Numerical experiments are given to illustrate the efficiency of the new algorithm.