On the spectra and pseudospectra of a class of non-self-adjoint random matrices and operators

Abstract

In this paper we develop and apply methods for the spectral analysis of non-self-adjoint tridiagonal innite and nite random matrices, and for the spectral analysis of analogous deterministic . We also propose a sequence of inclusion sets for which we show is convergent to , with the nth element of the sequence computable by calculating smallest singular values of (large numbers of) n n matrices. We propose similar convergent approximations for the 2-norm -pseudospectra of the innite random matrices, these approximations sandwiching the innite matrix pseudospectra from above and below.