TY - JOUR
T1 - Spectral computations for birth and death chains
AU - Chen, Guan-Yu
AU - Saloff-Coste, Laurent
PY - 2014
Y1 - 2014
N2 - 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.
AB - 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.
KW - Birth and death chains
KW - Spectrum
UR - http://www.scopus.com/inward/record.url?scp=84886571589&partnerID=8YFLogxK
U2 - 10.1016/j.spa.2013.10.002
DO - 10.1016/j.spa.2013.10.002
M3 - Article
AN - SCOPUS:84886571589
SN - 0304-4149
VL - 124
SP - 848
EP - 882
JO - Stochastic Processes and their Applications
JF - Stochastic Processes and their Applications
IS - 1
ER -