Fixed xml parse errors.

git-svn-id: https://svn.apache.org/repos/asf/jakarta/commons/proper/math/trunk@522436 13f79535-47bb-0310-9956-ffa450edef68
This commit is contained in:
Phil Steitz 2007-03-26 06:20:03 +00:00
parent dcb3ffa82c
commit b87e7190d5
3 changed files with 7 additions and 3 deletions

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@ -44,7 +44,9 @@
<p> <p>
One important class of estimation problems is weighted least squares problems. One important class of estimation problems is weighted least squares problems.
They basically consist in finding the values for some parameters p<sub>k</sub> They basically consist in finding the values for some parameters p<sub>k</sub>
such that a cost function J = &sum;(w<sub>i</sub> r<sub>i</sub><sup>2</sup>) such that a cost function J =
<!-- TODO: get entity for summation imported -->
sum(w<sub>i</sub> r<sub>i</sub><sup>2</sup>)
is minimized. The various r<sub>i</sub> terms represent the deviation is minimized. The various r<sub>i</sub> terms represent the deviation
r<sub>i</sub> = mes<sub>i</sub> - mod<sub>i</sub> between the measurements and r<sub>i</sub> = mes<sub>i</sub> - mod<sub>i</sub> between the measurements and
the parameterized models. The w<sub>i</sub> factors are the measurements weights, the parameterized models. The w<sub>i</sub> factors are the measurements weights,
@ -63,6 +65,7 @@
</li> </li>
<li> <li>
they are residuals based instead of generic cost functions based they are residuals based instead of generic cost functions based
</li>
</ul> </ul>
</p> </p>

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</p> </p>
<p> <p>
<table border="1" align="center"> <table border="1" align="center">
<tr BGCOLOR="#CCCCFF"><td colspan=2><font size="+2">Fixed Step Integrators</font></td></tr> <tr BGCOLOR="#CCCCFF"><td colspan="2"><font size="+2">Fixed Step Integrators</font></td></tr>
<tr BGCOLOR="#EEEEFF"><font size="+1"><td>Name</td><td>Order</td></font></tr> <tr BGCOLOR="#EEEEFF"><font size="+1"><td>Name</td><td>Order</td></font></tr>
<tr><td><a href="../apidocs/org/apache/commons/math/ode/EulerIntegrator.html">Euler</a></td><td>1</td></tr> <tr><td><a href="../apidocs/org/apache/commons/math/ode/EulerIntegrator.html">Euler</a></td><td>1</td></tr>
<tr><td><a href="../apidocs/org/apache/commons/math/ode/MidpointIntegrator.html">Midpoint</a></td><td>2</td></tr> <tr><td><a href="../apidocs/org/apache/commons/math/ode/MidpointIntegrator.html">Midpoint</a></td><td>2</td></tr>
@ -147,7 +147,7 @@
</p> </p>
<p> <p>
<table border="1" align="center"> <table border="1" align="center">
<tr BGCOLOR="#CCCCFF"><td colspan=3><font size="+2">Adaptive Stepsize Integrators</font></td></tr> <tr BGCOLOR="#CCCCFF"><td colspan="3"><font size="+2">Adaptive Stepsize Integrators</font></td></tr>
<tr BGCOLOR="#EEEEFF"><font size="+1"><td>Name</td><td>Integration Order</td><td>Error Estimation Order</td></font></tr> <tr BGCOLOR="#EEEEFF"><font size="+1"><td>Name</td><td>Integration Order</td><td>Error Estimation Order</td></font></tr>
<tr><td><a href="../apidocs/org/apache/commons/math/ode/HighamHall54Integrator.html">Higham and Hall</a></td><td>5</td><td>4</td></tr> <tr><td><a href="../apidocs/org/apache/commons/math/ode/HighamHall54Integrator.html">Higham and Hall</a></td><td>5</td><td>4</td></tr>
<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> <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> <li>
they do not rely on residuals-based quadratic cost functions but they do not rely on residuals-based quadratic cost functions but
handle any cost functions, including non-continuous ones! handle any cost functions, including non-continuous ones!
</li>
</ul> </ul>
</p> </p>
</subsection> </subsection>