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  <doc>
    <id>59</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>1991-09-25</completedDate>
    <publishedDate>1991-09-25</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">A Sharpened Condition Number Estimate for the BPX Preconditioner of Elliptic Finite Element Problems on Highly
Nonuniform Triangulations.</title>
    <abstract language="eng">In this paper it is shown that for highly nonuniformly refined triangulations the condition number of the BPX preconditioner for elliptic finite element problems grows at most linearly in the depth of refinement. This is achieved by viewing the computational available version of the BPX preconditioner as an abstract additive Schwarz method with exact solvers. {\bf AMS CLASSIFICATION:} 65F10, 65F35, 65N20, 65N30.</abstract>
    <identifier type="serial">SC-91-09</identifier>
    <identifier type="opus3-id">58</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-596</identifier>
    <enrichment key="SourceTitle">Is replaced by SC 92-01</enrichment>
    <author>Folkmar A. Bornemann</author>
    <series>
      <title>ZIB-Report</title>
      <number>SC-91-09</number>
    </series>
    <collection role="ddc" number="000">Informatik, Informationswissenschaft, allgemeine Werke</collection>
    <collection role="msc" number="65F10">Iterative methods for linear systems [See also 65N22]</collection>
    <collection role="msc" number="65F35">Matrix norms, conditioning, scaling [See also 15A12, 15A60]</collection>
    <collection role="msc" number="65N20">Ill-posed problems</collection>
    <collection role="msc" number="65N30">Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods</collection>
    <collection role="institutes" number="">ZIB Allgemein</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/59/SC-91-09.pdf</file>
  </doc>
</export-example>
