## Stable computation of probability densities for metastable dynamical systems

Please always quote using this URN: urn:nbn:de:0297-zib-9331

- Whenever the invariant stationary density of metastable dynamical systems decomposes into almost invariant partial densities, its computation as eigenvector of some transition probability matrix is an ill-conditioned problem. In order to avoid this computational difficulty, we suggest to apply an aggregation/disaggregation method which only addresses wellconditioned sub-problems and thus results in a stable algorithm. In contrast to existing methods, the aggregation step is done via a sampling algorithm which covers only small patches of the sampling space. Finally, the theoretical analysis is illustrated by two biomolecular examples.

Author: | Marcus Weber, Lionel Walter, Susanna Kube, Peter Deuflhard |
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Document Type: | ZIB-Report |

Tag: | aggregation/disaggregation; cluster analysis; domain decomposition; dynamical systems; metastability; molecular conformations; sampling |

MSC-Classification: | 62-XX STATISTICS / 62Hxx Multivariate analysis [See also 60Exx] / 62H30 Classification and discrimination; cluster analysis [See also 68T10] |

65-XX NUMERICAL ANALYSIS / 65Fxx Numerical linear algebra / 65F15 Eigenvalues, eigenvectors | |

82-XX STATISTICAL MECHANICS, STRUCTURE OF MATTER / 82Bxx Equilibrium statistical mechanics / 82B80 Numerical methods (Monte Carlo, series resummation, etc.) [See also 65-XX, 81T80] | |

Date of first Publication: | 2006/07/06 |

Series (Serial Number): | ZIB-Report (06-39) |

ZIB-Reportnumber: | 06-39 |

Published in: | Appeared in: SIAM J. Multisc. Mod. Sim. 2007, 6(2), pp. 396-416 |