Fixed xml parse errors.
git-svn-id: https://svn.apache.org/repos/asf/jakarta/commons/proper/math/trunk@522436 13f79535-47bb-0310-9956-ffa450edef68
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<p>
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<p>
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One important class of estimation problems is weighted least squares problems.
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One important class of estimation problems is weighted least squares problems.
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They basically consist in finding the values for some parameters p<sub>k</sub>
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They basically consist in finding the values for some parameters p<sub>k</sub>
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such that a cost function J = ∑(w<sub>i</sub> r<sub>i</sub><sup>2</sup>)
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such that a cost function J =
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<!-- TODO: get entity for summation imported -->
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sum(w<sub>i</sub> r<sub>i</sub><sup>2</sup>)
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is minimized. The various r<sub>i</sub> terms represent the deviation
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is minimized. The various r<sub>i</sub> terms represent the deviation
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r<sub>i</sub> = mes<sub>i</sub> - mod<sub>i</sub> between the measurements and
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r<sub>i</sub> = mes<sub>i</sub> - mod<sub>i</sub> between the measurements and
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the parameterized models. The w<sub>i</sub> factors are the measurements weights,
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the parameterized models. The w<sub>i</sub> factors are the measurements weights,
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</li>
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</li>
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<li>
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<li>
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they are residuals based instead of generic cost functions based
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they are residuals based instead of generic cost functions based
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</li>
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</ul>
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</ul>
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</p>
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</p>
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@ -136,7 +136,7 @@
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</p>
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</p>
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<p>
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<p>
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<table border="1" align="center">
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<table border="1" align="center">
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<tr BGCOLOR="#CCCCFF"><td colspan=2><font size="+2">Fixed Step Integrators</font></td></tr>
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<tr BGCOLOR="#CCCCFF"><td colspan="2"><font size="+2">Fixed Step Integrators</font></td></tr>
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<tr BGCOLOR="#EEEEFF"><font size="+1"><td>Name</td><td>Order</td></font></tr>
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<tr BGCOLOR="#EEEEFF"><font size="+1"><td>Name</td><td>Order</td></font></tr>
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<tr><td><a href="../apidocs/org/apache/commons/math/ode/EulerIntegrator.html">Euler</a></td><td>1</td></tr>
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<tr><td><a href="../apidocs/org/apache/commons/math/ode/EulerIntegrator.html">Euler</a></td><td>1</td></tr>
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<tr><td><a href="../apidocs/org/apache/commons/math/ode/MidpointIntegrator.html">Midpoint</a></td><td>2</td></tr>
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<tr><td><a href="../apidocs/org/apache/commons/math/ode/MidpointIntegrator.html">Midpoint</a></td><td>2</td></tr>
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</p>
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</p>
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<p>
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<p>
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<table border="1" align="center">
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<table border="1" align="center">
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<tr BGCOLOR="#CCCCFF"><td colspan=3><font size="+2">Adaptive Stepsize Integrators</font></td></tr>
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<tr BGCOLOR="#CCCCFF"><td colspan="3"><font size="+2">Adaptive Stepsize Integrators</font></td></tr>
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<tr BGCOLOR="#EEEEFF"><font size="+1"><td>Name</td><td>Integration Order</td><td>Error Estimation Order</td></font></tr>
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<tr BGCOLOR="#EEEEFF"><font size="+1"><td>Name</td><td>Integration Order</td><td>Error Estimation Order</td></font></tr>
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<tr><td><a href="../apidocs/org/apache/commons/math/ode/HighamHall54Integrator.html">Higham and Hall</a></td><td>5</td><td>4</td></tr>
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<tr><td><a href="../apidocs/org/apache/commons/math/ode/HighamHall54Integrator.html">Higham and Hall</a></td><td>5</td><td>4</td></tr>
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<tr><td><a href="../apidocs/org/apache/commons/math/ode/DormandPrince54Integrator.html">Dormand-Prince 5(4)</a></td><td>5</td><td>4</td></tr>
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<tr><td><a href="../apidocs/org/apache/commons/math/ode/DormandPrince54Integrator.html">Dormand-Prince 5(4)</a></td><td>5</td><td>4</td></tr>
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<li>
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<li>
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they do not rely on residuals-based quadratic cost functions but
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they do not rely on residuals-based quadratic cost functions but
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handle any cost functions, including non-continuous ones!
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handle any cost functions, including non-continuous ones!
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</li>
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</ul>
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</ul>
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</p>
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</p>
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</subsection>
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</subsection>
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