Piecewise continuous Toeplitz matrices and operators: slow approach to infinity

Report

The pseudospectra of banded finite dimensional Toeplitz matrices rapidly converge to the pseudospectra of the corresponding infinite dimensional operator. This exponential convergence makes a compelling case for analyzing pseudospectra of such Toeplitz matrices, not just eigenvalues. But what if the matrix is dense and its symbol has a jump discontinuity? The pseudospectra of the finite matrices still converge, but it is shown here that the rate is no longer exponential in the matrix dimension, only algebraic. The second and third authors were supported by UK Engineering and Physical Sciences Research Council Grant GR/M12414.

Authors: Boettcher, A; Embree, M; Trefethen, L

• Publisher: Unspecified
• Publication date: 2000-08-01