Author(s) :
David Fritzsche
,
Volker Mehrmann
,
Daniel Szyld
,
Elena Virnik
Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 15-2006
MSC 2000
- 15A18 Eigenvalues, singular values, and eigenvectors
-
15A51 Stochastic matrices
Abstract :
Being one of the key tools in conformation dynamics, the identification of
meta-stable states of Markov chains has been subject to extensive research in
recent years, especially when the Markov chains represent energy states of biomolecules. Some previous work on this topic involved the computation
of the eigenvalue cluster close to one, as well as the corresponding
eigenvectors and the stationary probability distribution of the associated stochastic
matrix. Later, since the eigenvalue cluster algorithm turned out to be non-robust, an optimisation approach was developed. As a possible less costly alternative, we present an SVD approach to identifying
meta-stable states of a stochastic matrix, where we only need
the second largest singular vector. We outline some theoretical background
and discuss the advantages of this strategy. Some simulated and real
numerical examples illustrate the effectiveness of the proposed algorithm.
Keywords :
Markov chains, conformation dynamics, singular value decomposition