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Main Title: An SVD approach to identifying meta-stable states of Markov chains
Author(s): Fritzsche, David
Mehrmann, Volker
Szyld, Daniel
Virnik, Elena
Type: Research Paper
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.
Subject(s): Markov chains
conformation dynamics
singular value decomposition
Issue Date: 4-Aug-2006
Date Available: 17-Dec-2021
Language Code: en
DDC Class: 510 Mathematik
MSC 2000: 15A18 Eigenvalues, singular values, and eigenvectors
15A51 Stochastic matrices
60J10 Markov chains with discrete parameter
60J20 Applications of discrete Markov processes (social mobility, learning theory, industrial processes, etc.)
65F15 Eigenvalues, eigenvectors
Series: Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin
Series Number: 2006, 15
ISSN: 2197-8085
TU Affiliation(s): Fak. 2 Mathematik und Naturwissenschaften » Inst. Mathematik
Appears in Collections:Technische Universität Berlin » Publications

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