Eigenvalues and quasi-eigenvalues of banded Toeplitz matrices: Some properties and applications (Q1862222)

The authors consider banded Toeplitz and quasi-Toeplitz matrices, as they may arise from certain discretisations of two-point boundary value problems. The intention is to find a good preconditioner, and the spectrum is important. As this is difficult to compute numerically, quasi-eigenvalues are considered. The connection with pseudo-spectra is nicely established. The paper concludes by constructing a preconditioner for a two-point boundary value problem and some numerical experiments.