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  <doc>
    <id>933</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2006-07-06</completedDate>
    <publishedDate>2006-07-06</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Stable computation of probability densities for metastable dynamical systems</title>
    <abstract language="eng">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.</abstract>
    <identifier type="serial">06-39</identifier>
    <identifier type="opus3-id">933</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-9331</identifier>
    <enrichment key="SourceTitle">Appeared in: SIAM J. Multisc. Mod. Sim. 2007, 6(2), pp. 396-416</enrichment>
    <author>Marcus Weber</author>
    <author>Lionel Walter</author>
    <author>Susanna Kube</author>
    <author>Peter Deuflhard</author>
    <series>
      <title>ZIB-Report</title>
      <number>06-39</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>dynamical systems</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>metastability</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>molecular conformations</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>cluster analysis</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>sampling</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>aggregation/disaggregation</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>domain decomposition</value>
    </subject>
    <collection role="ddc" number="000">Informatik, Informationswissenschaft, allgemeine Werke</collection>
    <collection role="msc" number="62H30">Classification and discrimination; cluster analysis [See also 68T10]</collection>
    <collection role="msc" number="65F15">Eigenvalues, eigenvectors</collection>
    <collection role="msc" number="82B80">Numerical methods (Monte Carlo, series resummation, etc.) [See also 65-XX, 81T80]</collection>
    <collection role="institutes" number="">ZIB Allgemein</collection>
    <collection role="persons" number="deuflhard">Deuflhard, Peter</collection>
    <collection role="persons" number="susanna.roeblitz">Röblitz, Susanna</collection>
    <collection role="persons" number="weber">Weber, Marcus</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/933/ZR-06-39.pdf</file>
  </doc>
</export-example>
