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      <header alignment="Center" color="#a9a9a9">&amp;[DATE] &amp;[TIME] - &amp;[FILENAME]</header>
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      <p bold="true">Gauss-Newton-Verfahren (Optimierer)</p>
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      <p href="Plugin Nonlinear Solvers.sm">Nonlinear Solvers</p>
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  <region id="2" top="54" color="#000000" bgColor="#ffffff">
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      <title lang="eng">
        <p>References</p>
      </title>
      <title lang="ger">
        <p>Informationsquellen</p>
      </title>
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    <region id="3" left="9" top="72" width="614" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
      <text lang="eng">
        <p>http://www2.imm.dtu.dk/pubdb/views/edoc_download.php/3215/pdf/imm3215.pdf</p>
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    <region id="4" left="9" top="99" width="556" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
      <text lang="eng">
        <p>http://www2.imm.dtu.dk/pubdb/views/publication_details.php?id=3215</p>
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    <region id="5" left="9" top="126" width="292" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
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        <p>http://www.brnt.eu/phd/node10.html</p>
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        <p>Algorithm</p>
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      <title lang="ger">
        <p>Algorithmus</p>
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    <region id="9" left="108" top="180" width="431" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
      <text lang="ger">
        <p>Vektorwerte Funktion eines vektorwertigen Arguments</p>
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    <region id="10" left="18" top="207" width="29" height="32" color="#000000" bgColor="#ffffff" fontSize="10">
      <math>
        <input>
          <e type="operand">x.0</e>
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      </math>
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    <region id="11" left="108" top="207" width="107" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
      <text lang="ger">
        <p>Startvektor </p>
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    <region id="12" left="18" top="243" width="37" height="32" color="#000000" bgColor="#ffffff" fontSize="10">
      <math>
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          <e type="operand">ε.Δx</e>
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    <region id="13" left="108" top="243" width="349" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
      <text lang="ger">
        <p>Toleranz auf die iterative Änderung von x</p>
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    <region id="14" left="18" top="279" width="45" height="32" color="#000000" bgColor="#ffffff" fontSize="10">
      <math>
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          <e type="operand">n.max</e>
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      </math>
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    <region id="15" left="108" top="279" width="251" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
      <text lang="ger">
        <p>Maximale Zahl von Iterationen</p>
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    <region id="16" left="18" top="315" width="28" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
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    <region id="17" left="108" top="315" width="393" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
      <text lang="ger">
        <p>Skalierung: 0 -&gt; α=1, "GSS" -&gt; GSS-Line-Search </p>
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          <e type="operand">3</e>
          <e type="operand">1</e>
          <e type="function" preserve="true" args="5">line</e>
          <e type="function" preserve="true" args="3">if</e>
          <e type="operand">3</e>
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          <e type="operand">1</e>
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          <e type="operand">1</e>
          <e type="function" preserve="true" args="4">mat</e>
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          <e type="operand">1</e>
          <e type="function" preserve="true" args="8">line</e>
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      <p>Testfunktion </p>
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        <e type="function" args="1">Rosenbrock</e>
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        <e type="operand">1</e>
        <e type="function" preserve="true" args="2">el</e>
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        <e type="operand">α</e>
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        <e type="function" preserve="true" args="2">el</e>
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        <e type="operand">2</e>
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        <e type="function" preserve="true" args="4">mat</e>
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    <text lang="ger">
      <p>Vektorwertig, vektorielles
Argument</p>
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        <e type="operand">x</e>
        <e type="operator" args="2">-</e>
        <e type="operand">α</e>
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        <e type="operand">y</e>
        <e type="operand">x</e>
        <e type="operand">2</e>
        <e type="operator" args="2">^</e>
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        <e type="bracket">(</e>
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        <e type="operand">2</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="4">sys</e>
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      <p>Listenwertig, 2 skalare 
Argumente</p>
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        <e type="function" args="1">Rosenbrock</e>
        <e type="operand">200090</e>
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        <e type="operand">200</e>
        <e type="operand">2</e>
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        <e type="operand">1</e>
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        <e type="function" preserve="true" args="4">mat</e>
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        <e type="function" args="1">Rosenbrock</e>
        <e type="operand">0.5</e>
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        <e type="operand">1.5</e>
        <e type="operand">2</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="4">sys</e>
        <e type="operand">0.01</e>
        <e type="function" preserve="true" args="3">GaussNewton.GSS</e>
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        <e type="operand">1.00001</e>
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        <e type="function" preserve="true" args="4">sys</e>
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      <p bold="true">Integrierte Lösungszuweisung</p>
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      <input>
        <e type="operand">#1</e>
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        <e type="operand">x</e>
        <e type="operand">10</e>
        <e type="operand">10</e>
        <e type="operand">2</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="4">mat</e>
        <e type="operator" args="2">≡</e>
        <e type="operand">0.0002</e>
        <e type="function" preserve="true" args="3">GaussNewton</e>
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        <e type="operand">1</e>
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      <result action="numeric">
        <e type="operand">1</e>
        <e type="operand">1</e>
        <e type="operand">2</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="4">mat</e>
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        <e type="operand">10</e>
        <e type="operand">10</e>
        <e type="operand">2</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="4">sys</e>
        <e type="operator" args="2">≡</e>
        <e type="operand">0.0002</e>
        <e type="function" preserve="true" args="3">GaussNewton</e>
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        <e type="operand">1</e>
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        <e type="operand">10</e>
        <e type="operand">10</e>
        <e type="operand">2</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="4">sys</e>
        <e type="operator" args="2">≡</e>
        <e type="operand">0.0002</e>
        <e type="function" preserve="true" args="3">GaussNewton</e>
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      <result action="numeric">
        <e type="operand">1</e>
        <e type="operand">1</e>
        <e type="operand">2</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="4">sys</e>
      </result>
    </math>
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  <region id="36" left="432" top="1260" width="62" height="44" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">x</e>
      </input>
      <result action="numeric">
        <e type="operand">1</e>
        <e type="operand">1</e>
        <e type="operand">2</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="4">sys</e>
      </result>
    </math>
  </region>
  <region id="37" left="18" top="1305" width="435" height="62" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">#1</e>
        <e type="operand">#2</e>
        <e type="function" args="2">Rosenbrock</e>
        <e type="operand">x.1</e>
        <e type="operand">10</e>
        <e type="operator" args="2">≡</e>
        <e type="operand">x.2</e>
        <e type="operand">10</e>
        <e type="operator" args="2">≡</e>
        <e type="operand">2</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="4">sys</e>
        <e type="operand">0.0002</e>
        <e type="function" preserve="true" args="3">GaussNewton</e>
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      <result action="numeric">
        <e type="operand">1</e>
        <e type="operand">1</e>
        <e type="operand">2</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="4">sys</e>
      </result>
    </math>
  </region>
  <region id="38" left="441" top="1323" width="62" height="32" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">x.1</e>
      </input>
      <result action="numeric">
        <e type="operand">1</e>
      </result>
    </math>
  </region>
  <region id="39" left="513" top="1323" width="62" height="32" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">x.2</e>
      </input>
      <result action="numeric">
        <e type="operand">1</e>
      </result>
    </math>
  </region>
  <region id="40" left="18" top="1377" width="193" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p bold="true">Quadratische Gleichung</p>
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  </region>
  <region id="41" left="18" top="1404" width="106" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">x</e>
        <e type="function" preserve="true" args="1">Clear</e>
      </input>
      <result action="numeric">
        <e type="operand">1</e>
      </result>
    </math>
  </region>
  <region id="42" left="18" top="1431" width="365" height="35" color="#000000" bgColor="#ffffff" fontSize="10">
    <math decimalPlaces="5">
      <input>
        <e type="operand">x</e>
        <e type="operand">2</e>
        <e type="operator" args="2">^</e>
        <e type="operand">4</e>
        <e type="operand">x</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">+</e>
        <e type="operand">3</e>
        <e type="operator" args="2">+</e>
        <e type="operand">1</e>
        <e type="operand">0.001</e>
        <e type="function" preserve="true" args="3">GaussNewton</e>
      </input>
      <result action="numeric">
        <e type="operand">0.99997</e>
        <e type="operator" args="1">-</e>
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    </math>
  </region>
  <region id="43" left="18" top="1485" width="240" height="158" color="#000000" bgColor="#ffffff" fontSize="10">
    <plot type="2d" render="lines" scale_x="4.59497298635722" scale_y="4.59497298635722" scale_z="4.59497298635722" rotate_x="0" rotate_y="0" rotate_z="0" transpose_x="78" transpose_y="21" transpose_z="0">
      <input>
        <e type="operand">x</e>
        <e type="operand">2</e>
        <e type="operator" args="2">^</e>
        <e type="operand">4</e>
        <e type="operand">x</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">+</e>
        <e type="operand">3</e>
        <e type="operator" args="2">+</e>
      </input>
    </plot>
  </region>
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