Spectral computations for birth and death chains

Guan-Yu Chen and Laurent Saloff-Coste

Stochastic Processes and their Applications, 2014, vol. 124, issue 1, 848-882

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 n2 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.

Keywords: Birth and death chains; Spectrum (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1016/j.spa.2013.10.002

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