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      <header alignment="Center" color="#a9a9a9">&amp;[DATE] &amp;[TIME] - &amp;[FILENAME]</header>
      <footer alignment="Center" color="#a9a9a9">&amp;[PAGENUM] / &amp;[COUNT]</footer>
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  <region id="0" left="9" top="18" width="267" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p bold="true">Example 2: Quadratic parabola</p>
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    <text lang="ger">
      <p bold="true">Beispiel 2 Quadratische Parabel</p>
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      <p href="Plugin Nonlinear Solvers.sm">Nonlinear Solvers</p>
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      <p href="Handbook.sm">Contents</p>
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    <text lang="ger">
      <p href="Handbook.sm">Inhalt</p>
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        <p>Roots</p>
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        <p>Nullstellen</p>
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          <e type="operand">2</e>
          <e type="operator" args="1">-</e>
          <e type="operand">1</e>
          <e type="operand">ε.f</e>
          <e type="operand">0</e>
          <e type="operand">0</e>
          <e type="operand">1</e>
          <e type="operand">0</e>
          <e type="operand">0</e>
          <e type="function" preserve="true" args="9">Ridder</e>
        </input>
        <result action="numeric">
          <e type="operand">1.000016</e>
          <e type="operator" args="1">-</e>
          <e type="operand">4</e>
          <e type="operand">1</e>
          <e type="operand">1</e>
          <e type="function" preserve="true" args="3">mat</e>
          <e type="operand">2</e>
          <e type="operand">1</e>
          <e type="function" preserve="true" args="4">mat</e>
        </result>
      </math>
    </region>
    <region id="32" left="459" top="828" width="238" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
      <math decimalPlaces="6">
        <input>
          <e type="operand">f</e>
          <e type="operand">2</e>
          <e type="operator" args="1">-</e>
          <e type="operand">1</e>
          <e type="function" preserve="true" args="3">Ridder</e>
        </input>
        <result action="numeric">
          <e type="operand">1.000016</e>
          <e type="operator" args="1">-</e>
        </result>
      </math>
    </region>
    <region id="33" left="9" top="864" width="408" height="46" color="#000000" bgColor="#ffffff" fontSize="10">
      <math decimalPlaces="6">
        <input>
          <e type="operand">f</e>
          <e type="operand">0</e>
          <e type="operand">0.5</e>
          <e type="operand">ε.f</e>
          <e type="operand">0</e>
          <e type="operand">0</e>
          <e type="operand">1</e>
          <e type="operand">0</e>
          <e type="operand">0</e>
          <e type="function" preserve="true" args="9">Secant</e>
        </input>
        <result action="numeric">
          <e type="operand">0.999991</e>
          <e type="operator" args="1">-</e>
          <e type="operand">4</e>
          <e type="operand">1</e>
          <e type="operand">1</e>
          <e type="function" preserve="true" args="3">mat</e>
          <e type="operand">2</e>
          <e type="operand">1</e>
          <e type="function" preserve="true" args="4">mat</e>
        </result>
      </math>
    </region>
    <region id="34" left="459" top="873" width="255" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
      <math decimalPlaces="6">
        <input>
          <e type="operand">f</e>
          <e type="operand">2</e>
          <e type="operator" args="1">-</e>
          <e type="operand">0.5</e>
          <e type="function" preserve="true" args="3">Secant</e>
        </input>
        <result action="numeric">
          <e type="operand">0.999967</e>
          <e type="operator" args="1">-</e>
        </result>
      </math>
    </region>
    <region id="35" top="909" color="#000000" bgColor="#ffffff">
      <area terminator="true" />
    </region>
  </region>
  <region id="36" top="927" color="#000000" bgColor="#ffffff">
    <area collapsed="false">
      <title lang="eng">
        <p>Minimum</p>
      </title>
      <title lang="ger">
        <p>Scheitelpunkt</p>
      </title>
    </area>
    <region id="37" left="18" top="954" width="101" height="32" color="#000000" bgColor="#ffffff" fontSize="10">
      <math>
        <input>
          <e type="operand">ε.Δx</e>
          <e type="operand">0.0001</e>
          <e type="operator" args="2">:</e>
        </input>
      </math>
    </region>
    <region id="38" left="18" top="981" width="475" height="46" color="#000000" bgColor="#ffffff" fontSize="10">
      <math>
        <input>
          <e type="operand">f</e>
          <e type="operand">10</e>
          <e type="operator" args="1">-</e>
          <e type="operand">0</e>
          <e type="operand">ε.Δx</e>
          <e type="operand">0</e>
          <e type="operand">1</e>
          <e type="operand">0</e>
          <e type="operand">0</e>
          <e type="function" preserve="true" args="8">GoldenSectionSearch.min</e>
        </input>
        <result action="numeric">
          <e type="operand">2</e>
          <e type="operator" args="1">-</e>
          <e type="operand">24</e>
          <e type="operand">1</e>
          <e type="operand">1</e>
          <e type="function" preserve="true" args="3">mat</e>
          <e type="operand">2</e>
          <e type="operand">1</e>
          <e type="function" preserve="true" args="4">mat</e>
        </result>
      </math>
    </region>
    <region id="39" left="513" top="999" width="37" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
      <math>
        <input>
          <e type="operand">min</e>
        </input>
      </math>
    </region>
    <region id="40" left="18" top="1026" width="433" height="48" color="#000000" bgColor="#ffffff" fontSize="10">
      <math>
        <input>
          <e type="operand">f</e>
          <e type="operand">1</e>
          <e type="operand">1</e>
          <e type="operand">1</e>
          <e type="function" preserve="true" args="3">mat</e>
          <e type="operand">0</e>
          <e type="operand">1</e>
          <e type="operand">1</e>
          <e type="function" preserve="true" args="3">mat</e>
          <e type="operand">1</e>
          <e type="operand">2</e>
          <e type="function" preserve="true" args="4">mat</e>
          <e type="operand">ε.f</e>
          <e type="operand">0</e>
          <e type="operand">0</e>
          <e type="operand">0</e>
          <e type="operand">0</e>
          <e type="operand">1</e>
          <e type="operand">0</e>
          <e type="operand">0</e>
          <e type="function" preserve="true" args="10">NelderMead</e>
        </input>
        <result action="numeric">
          <e type="operand">0</e>
          <e type="operand">1</e>
          <e type="operand">1</e>
          <e type="function" preserve="true" args="3">mat</e>
          <e type="operand">1</e>
          <e type="operand">1</e>
          <e type="operand">1</e>
          <e type="function" preserve="true" args="3">mat</e>
          <e type="operand">2</e>
          <e type="operand">1</e>
          <e type="function" preserve="true" args="4">mat</e>
        </result>
      </math>
    </region>
    <region id="41" left="513" top="1044" width="168" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
      <text lang="ger">
        <p>not coping with 1D?</p>
      </text>
    </region>
    <region id="42" left="18" top="1080" width="352" height="46" color="#000000" bgColor="#ffffff" fontSize="10">
      <math>
        <input>
          <e type="operand">f</e>
          <e type="operand">0</e>
          <e type="operand">ε.Δx</e>
          <e type="operand">0</e>
          <e type="operand">10</e>
          <e type="operator" args="1">-</e>
          <e type="operand">0</e>
          <e type="operand">0</e>
          <e type="function" preserve="true" args="7">GaussNewton</e>
        </input>
        <result action="numeric">
          <e type="operand">1</e>
          <e type="operator" args="1">-</e>
          <e type="operand">4</e>
          <e type="operand">1</e>
          <e type="operand">1</e>
          <e type="function" preserve="true" args="3">mat</e>
          <e type="operand">2</e>
          <e type="operand">1</e>
          <e type="function" preserve="true" args="4">mat</e>
        </result>
      </math>
    </region>
    <region id="43" left="513" top="1089" width="118" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
      <text lang="ger">
        <p>min of square</p>
      </text>
    </region>
    <region id="44" left="18" top="1125" width="375" height="46" color="#000000" bgColor="#ffffff" fontSize="10">
      <math>
        <input>
          <e type="operand">f</e>
          <e type="operand">0</e>
          <e type="operand">ε.Δx</e>
          <e type="operand">h</e>
          <e type="operand">0</e>
          <e type="operand">1</e>
          <e type="operand">0</e>
          <e type="operand">0</e>
          <e type="function" preserve="true" args="8">GaussNewton.CD</e>
        </input>
        <result action="numeric">
          <e type="operand">1</e>
          <e type="operator" args="1">-</e>
          <e type="operand">4</e>
          <e type="operand">1</e>
          <e type="operand">1</e>
          <e type="function" preserve="true" args="3">mat</e>
          <e type="operand">2</e>
          <e type="operand">1</e>
          <e type="function" preserve="true" args="4">mat</e>
        </result>
      </math>
    </region>
    <region id="45" left="513" top="1134" width="118" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
      <text lang="ger">
        <p>min of square</p>
      </text>
    </region>
    <region id="46" left="18" top="1170" width="377" height="46" color="#000000" bgColor="#ffffff" fontSize="10">
      <math>
        <input>
          <e type="operand">f</e>
          <e type="operand">0</e>
          <e type="operand">ε.Δx</e>
          <e type="operand">0</e>
          <e type="operand">1</e>
          <e type="operand">0</e>
          <e type="operand">0</e>
          <e type="function" preserve="true" args="7">GaussNewton.GSS</e>
        </input>
        <result action="numeric">
          <e type="operand">2</e>
          <e type="operator" args="1">-</e>
          <e type="operand">100</e>
          <e type="operand">1</e>
          <e type="operand">1</e>
          <e type="function" preserve="true" args="3">mat</e>
          <e type="operand">2</e>
          <e type="operand">1</e>
          <e type="function" preserve="true" args="4">mat</e>
        </result>
      </math>
    </region>
    <region id="47" left="513" top="1179" width="217" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
      <text lang="ger">
        <p>min, tolerance not obeyed</p>
      </text>
    </region>
    <region id="48" left="513" top="1206" width="226" height="56" color="#000000" bgColor="#ffffff" fontSize="10">
      <text lang="ger">
        <p>min, tolerance not obeyed,
numeric 0/0 problem with
small Δx</p>
      </text>
    </region>
    <region id="49" left="18" top="1215" width="449" height="46" color="#000000" bgColor="#ffffff" fontSize="10">
      <math>
        <input>
          <e type="operand">f</e>
          <e type="operand">0</e>
          <e type="operand">ε.Δx</e>
          <e type="operand">h</e>
          <e type="operand">0</e>
          <e type="operand">1</e>
          <e type="operand">0</e>
          <e type="operand">0</e>
          <e type="function" preserve="true" args="8">GaussNewton.GSS;CD</e>
        </input>
        <result action="numeric">
          <e type="operand">2.4287</e>
          <e type="operator" args="1">-</e>
          <e type="operand">100</e>
          <e type="operand">1</e>
          <e type="operand">1</e>
          <e type="function" preserve="true" args="3">mat</e>
          <e type="operand">2</e>
          <e type="operand">1</e>
          <e type="function" preserve="true" args="4">mat</e>
        </result>
      </math>
    </region>
    <region id="50" left="18" top="1260" width="402" height="46" color="#000000" bgColor="#ffffff" fontSize="10">
      <math>
        <input>
          <e type="operand">f</e>
          <e type="operand">0</e>
          <e type="operand">ε.Δx</e>
          <e type="operand">100</e>
          <e type="operand">1</e>
          <e type="operand">0</e>
          <e type="operand">0</e>
          <e type="function" preserve="true" args="7">GradientDescent</e>
        </input>
        <result action="numeric">
          <e type="operand">4</e>
          <e type="operator" args="1">-</e>
          <e type="operand">100</e>
          <e type="operand">1</e>
          <e type="operand">1</e>
          <e type="function" preserve="true" args="3">mat</e>
          <e type="operand">2</e>
          <e type="operand">1</e>
          <e type="function" preserve="true" args="4">mat</e>
        </result>
      </math>
    </region>
    <region id="51" left="513" top="1269" width="202" height="40" color="#000000" bgColor="#ffffff" fontSize="10">
      <text lang="ger">
        <p>oscillating independent
of initial guess</p>
      </text>
    </region>
    <region id="52" left="18" top="1305" width="393" height="46" color="#000000" bgColor="#ffffff" fontSize="10">
      <math>
        <input>
          <e type="operand">f</e>
          <e type="operand">0</e>
          <e type="operand">ε.Δx</e>
          <e type="operand">0</e>
          <e type="operand">1</e>
          <e type="operand">0</e>
          <e type="operand">0</e>
          <e type="function" preserve="true" args="7">GradientDescent.GSS</e>
        </input>
        <result action="numeric">
          <e type="operand">2</e>
          <e type="operator" args="1">-</e>
          <e type="operand">1</e>
          <e type="operand">1</e>
          <e type="operand">1</e>
          <e type="function" preserve="true" args="3">mat</e>
          <e type="operand">2</e>
          <e type="operand">1</e>
          <e type="function" preserve="true" args="4">mat</e>
        </result>
      </math>
    </region>
    <region id="53" left="513" top="1314" width="37" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
      <math>
        <input>
          <e type="operand">min</e>
        </input>
      </math>
    </region>
    <region id="54" left="18" top="1350" width="409" height="46" color="#000000" bgColor="#ffffff" fontSize="10">
      <math>
        <input>
          <e type="operand">f</e>
          <e type="operand">0</e>
          <e type="operand">ε.Δx</e>
          <e type="operand">0</e>
          <e type="operand">1</e>
          <e type="operand">0</e>
          <e type="operand">0</e>
          <e type="function" preserve="true" args="7">LevenbergMarquardt</e>
        </input>
        <result action="numeric">
          <e type="operand">1</e>
          <e type="operator" args="1">-</e>
          <e type="operand">100</e>
          <e type="operand">1</e>
          <e type="operand">1</e>
          <e type="function" preserve="true" args="3">mat</e>
          <e type="operand">2</e>
          <e type="operand">1</e>
          <e type="function" preserve="true" args="4">mat</e>
        </result>
      </math>
    </region>
    <region id="55" left="513" top="1350" width="209" height="40" color="#000000" bgColor="#ffffff" fontSize="10">
      <text lang="ger">
        <p>min of square, tolerance
not obeyed</p>
      </text>
    </region>
    <region id="56" left="18" top="1395" width="450" height="46" color="#000000" bgColor="#ffffff" fontSize="10">
      <math>
        <input>
          <e type="operand">f</e>
          <e type="operand">0</e>
          <e type="operand">ε.Δx</e>
          <e type="operand">h</e>
          <e type="operand">0</e>
          <e type="operand">1</e>
          <e type="operand">0</e>
          <e type="operand">0</e>
          <e type="function" preserve="true" args="8">LevenbergMarquardt.CD</e>
        </input>
        <result action="numeric">
          <e type="operand">1</e>
          <e type="operator" args="1">-</e>
          <e type="operand">100</e>
          <e type="operand">1</e>
          <e type="operand">1</e>
          <e type="function" preserve="true" args="3">mat</e>
          <e type="operand">2</e>
          <e type="operand">1</e>
          <e type="function" preserve="true" args="4">mat</e>
        </result>
      </math>
    </region>
    <region id="57" left="513" top="1395" width="209" height="40" color="#000000" bgColor="#ffffff" fontSize="10">
      <text lang="ger">
        <p>min of square, tolerance
not obeyed</p>
      </text>
    </region>
    <region id="58" left="18" top="1440" width="277" height="46" color="#000000" bgColor="#ffffff" fontSize="10">
      <math>
        <input>
          <e type="operand">f</e>
          <e type="operand">0</e>
          <e type="operand">ε.Δx</e>
          <e type="operand">0</e>
          <e type="operand">1</e>
          <e type="operand">0</e>
          <e type="operand">0</e>
          <e type="function" preserve="true" args="7">NCGM</e>
        </input>
        <result action="numeric">
          <e type="operand">2</e>
          <e type="operator" args="1">-</e>
          <e type="operand">0</e>
          <e type="operand">1</e>
          <e type="operand">1</e>
          <e type="function" preserve="true" args="3">mat</e>
          <e type="operand">2</e>
          <e type="operand">1</e>
          <e type="function" preserve="true" args="4">mat</e>
        </result>
      </math>
    </region>
    <region id="59" left="513" top="1449" width="37" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
      <math>
        <input>
          <e type="operand">min</e>
        </input>
      </math>
    </region>
    <region id="60" left="18" top="1485" width="318" height="46" color="#000000" bgColor="#ffffff" fontSize="10">
      <math>
        <input>
          <e type="operand">f</e>
          <e type="operand">0</e>
          <e type="operand">ε.Δx</e>
          <e type="operand">h</e>
          <e type="operand">0</e>
          <e type="operand">1</e>
          <e type="operand">0</e>
          <e type="operand">0</e>
          <e type="function" preserve="true" args="8">NCGM.CD</e>
        </input>
        <result action="numeric">
          <e type="operand">2</e>
          <e type="operator" args="1">-</e>
          <e type="operand">0</e>
          <e type="operand">1</e>
          <e type="operand">1</e>
          <e type="function" preserve="true" args="3">mat</e>
          <e type="operand">2</e>
          <e type="operand">1</e>
          <e type="function" preserve="true" args="4">mat</e>
        </result>
      </math>
    </region>
    <region id="61" left="513" top="1485" width="37" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
      <math>
        <input>
          <e type="operand">min</e>
        </input>
      </math>
    </region>
    <region id="62" left="18" top="1539" width="276" height="34" color="#000000" bgColor="#ffffff" fontSize="10">
      <math error="69">
        <input>
          <e type="operand">f</e>
          <e type="operand">10</e>
          <e type="operator" args="1">-</e>
          <e type="operand">ε.Δx</e>
          <e type="operand">0</e>
          <e type="operand">1</e>
          <e type="operand">0</e>
          <e type="operand">0</e>
          <e type="function" preserve="true" args="7">NCGM</e>
        </input>
        <result action="numeric">
          <e type="operand">#</e>
        </result>
      </math>
    </region>
    <region id="63" left="513" top="1575" width="180" height="56" color="#000000" bgColor="#ffffff" fontSize="10">
      <text lang="ger">
        <p>strange dependence
on initial value and 
tolerance</p>
      </text>
    </region>
    <region id="64" left="18" top="1584" width="282" height="34" color="#000000" bgColor="#ffffff" fontSize="10">
      <math error="69">
        <input>
          <e type="operand">f</e>
          <e type="operand">0</e>
          <e type="operand">10</e>
          <e type="operand">ε.Δx</e>
          <e type="operator" args="2">*</e>
          <e type="operand">0</e>
          <e type="operand">1</e>
          <e type="operand">0</e>
          <e type="operand">0</e>
          <e type="function" preserve="true" args="7">NCGM</e>
        </input>
        <result action="numeric">
          <e type="operand">#</e>
        </result>
      </math>
    </region>
    <region id="65" left="18" top="1629" width="323" height="34" color="#000000" bgColor="#ffffff" fontSize="10">
      <math error="69">
        <input>
          <e type="operand">f</e>
          <e type="operand">0</e>
          <e type="operand">10</e>
          <e type="operand">ε.Δx</e>
          <e type="operator" args="2">*</e>
          <e type="operand">h</e>
          <e type="operand">0</e>
          <e type="operand">1</e>
          <e type="operand">0</e>
          <e type="operand">0</e>
          <e type="function" preserve="true" args="8">NCGM.CD</e>
        </input>
        <result action="numeric">
          <e type="operand">#</e>
        </result>
      </math>
    </region>
    <region id="66" left="18" top="1674" width="343" height="46" color="#000000" bgColor="#ffffff" fontSize="10">
      <math>
        <input>
          <e type="operand">f</e>
          <e type="operand">0</e>
          <e type="operand">ε.Δx</e>
          <e type="operand">0</e>
          <e type="operand">1</e>
          <e type="operand">0</e>
          <e type="operand">0</e>
          <e type="function" preserve="true" args="7">NewtonMethod</e>
        </input>
        <result action="numeric">
          <e type="operand">2</e>
          <e type="operator" args="1">-</e>
          <e type="operand">1</e>
          <e type="operand">1</e>
          <e type="operand">1</e>
          <e type="function" preserve="true" args="3">mat</e>
          <e type="operand">2</e>
          <e type="operand">1</e>
          <e type="function" preserve="true" args="4">mat</e>
        </result>
      </math>
    </region>
    <region id="67" left="513" top="1683" width="37" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
      <math>
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      <p italic="true">M. Kraska, 2013-07-01 </p>
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