1 Ocak 2015 Dergi makalesi Açık Erişim

Dayar, Tugrul; Orhan, M. Can

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  <identifier identifierType="URL">https://aperta.ulakbim.gov.tr/record/78889</identifier>
  <creators>
    <creator>
      <creatorName>Dayar, Tugrul</creatorName>
      <givenName>Tugrul</givenName>
      <familyName>Dayar</familyName>
      <affiliation>Bilkent Univ, Dept Comp Engn, TR-06800 Ankara, Turkey</affiliation>
    </creator>
    <creator>
      <creatorName>Orhan, M. Can</creatorName>
      <givenName>M. Can</givenName>
      <familyName>Orhan</familyName>
      <affiliation>Bilkent Univ, Dept Comp Engn, TR-06800 Ankara, Turkey</affiliation>
    </creator>
  </creators>
  <titles>
    <title>On Vector-Kronecker Product Multiplication With Rectangular Factors</title>
  </titles>
  <publisher>Aperta</publisher>
  <publicationYear>2015</publicationYear>
  <dates>
    <date dateType="Issued">2015-01-01</date>
  </dates>
  <resourceType resourceTypeGeneral="Text">Journal article</resourceType>
  <alternateIdentifiers>
    <alternateIdentifier alternateIdentifierType="url">https://aperta.ulakbim.gov.tr/record/78889</alternateIdentifier>
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  <relatedIdentifiers>
    <relatedIdentifier relatedIdentifierType="DOI" relationType="IsIdenticalTo">10.1137/140980326</relatedIdentifier>
  </relatedIdentifiers>
  <rightsList>
    <rights rightsURI="http://www.opendefinition.org/licenses/cc-by">Creative Commons Attribution</rights>
    <rights rightsURI="info:eu-repo/semantics/openAccess">Open Access</rights>
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  <descriptions>
    <description descriptionType="Abstract">The infinitesimal generator matrix underlying a multidimensional Markov chain can be represented compactly by using sums of Kronecker products of small rectangular matrices. For such compact representations, analysis methods based on vector-Kronecker product multiplication need to be employed. When the factors in the Kronecker product terms are relatively dense, vector-Kronecker product multiplication can be performed efficiently by the shuffle algorithm. When the factors are relatively sparse, it may be more efficient to obtain nonzero elements of the generator matrix in Kronecker form on the fly and multiply them with corresponding elements of the vector. This work proposes a modification to the shuffle algorithm that multiplies relevant elements of the vector with submatrices of factors in which zero rows and columns are omitted. This approach avoids unnecessary floating-point operations that evaluate to zero during the course of the multiplication and possibly reduces the amount of memory used. Numerical experiments on a large number of models indicate that in many cases the modified shuffle algorithm performs a smaller number of floating-point operations than the shuffle algorithm and the algorithm that generates nonzeros on the fly, sometimes with a minimum number of floating-point operations and as little of memory possible.</description>
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