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  <doc>
    <id>700</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2002-10-24</completedDate>
    <publishedDate>2002-10-24</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Affine Invariant Adaptive Newton Codes for Discretized PDEs</title>
    <abstract language="eng">The paper deals with three different Newton algorithms that have recently been worked out in the general frame of affine invariance. Of particular interest is their performance in the numerical solution of discretized boundary value problems (BVPs) for nonlinear partial differential equations (PDEs). Exact Newton methods, where the arising linear systems are solved by direct elimination, and inexact Newton methods, where an inner iteration is used instead, are synoptically presented, both in affine invariant convergence theory and in numerical experiments. The three types of algorithms are: (a) affine covariant (formerly just called affine invariant) Newton algorithms, oriented toward the iterative errors, (b) affine contravariant Newton algorithms, based on iterative residual norms, and (c) affine conjugate Newton algorithms for convex optimization problems and discrete nonlinear elliptic PDEs.</abstract>
    <identifier type="serial">02-33</identifier>
    <identifier type="opus3-id">701</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-7005</identifier>
    <enrichment key="SourceTitle">Appeared in: P. Deuflhard: Newton Methods for Nonlinear Problems. Affine Invariance and Adaptive Algorithms. Springer 2004. Series Computational Mathemtics, 35</enrichment>
    <author>Peter Deuflhard</author>
    <author>Ulrich Nowak</author>
    <author>Martin Weiser</author>
    <series>
      <title>ZIB-Report</title>
      <number>02-33</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Affine invariant Newton methods</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>global Newton methods</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>inexact Newton methods</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>adaptive trust region methods</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>nonlinear partial differential equa</value>
    </subject>
    <collection role="ddc" number="000">Informatik, Informationswissenschaft, allgemeine Werke</collection>
    <collection role="msc" number="65H10">Systems of equations</collection>
    <collection role="msc" number="65H20">Global methods, including homotopy approaches [See also 58C30, 90C30]</collection>
    <collection role="institutes" number="compmed">Computational Medicine</collection>
    <collection role="persons" number="deuflhard">Deuflhard, Peter</collection>
    <collection role="persons" number="weiser">Weiser, Martin</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/700/ZR-02-33.ps</file>
    <file>https://opus4.kobv.de/opus4-zib/files/700/ZR-02-33.pdf</file>
  </doc>
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