Spectral computations for birth and death chains

Guan-Yu Chen; Laurent Saloff-Coste

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arXiv · 1305.0353

Spectral computations for birth and death chains

Guan-Yu Chen·Laurent Saloff-Coste

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Abstract

We consider the spectrum of birth and death chains on a $n$-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.

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Guan-Yu Chen, Laurent Saloff-Coste. 2013-05-02. Spectral computations for birth and death chains. https://arxiv.org/abs/1305.0353

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