Spectral computations for birth and death chains

Abstract

We consider the spectrum of birth and death chains on an n-path. An iterative scheme is proposed to compute any eigenvalue with exponential convergence rate independent of n. This allows one to determine the whole spectrum in order n(2) elementary operations. Using the same idea, we also provide a lower bound on the spectral gap, which is of the correct order on some classes of examples. (C) 2013 Elsevier B.V. All rights reserved.