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mhjensen committed Feb 22, 2024
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<!-- tocinfo
{'highest level': 2,
'sections': [('Overview of week 8', 2, None, 'overview-of-week-8'),
'sections': [('Overview', 2, None, 'overview'),
("Brief reminder on Newton-Raphson's method",
2,
None,
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('Steepest descent method', 2, None, 'steepest-descent-method'),
('Steepest descent method', 2, None, 'steepest-descent-method'),
('Final expressions', 2, None, 'final-expressions'),
('Code examples for steepest descent',
('Our simple $2\\times 2$ example',
2,
None,
'code-examples-for-steepest-descent'),
'our-simple-2-times-2-example'),
('Derivatives and more', 2, None, 'derivatives-and-more'),
('Simple codes for steepest descent and conjugate gradient '
'using a $2\\times 2$ matrix, in c++, Python code to come',
2,
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<li class="dropdown">
<a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
<ul class="dropdown-menu">
<!-- navigation toc: --> <li><a href="._week6-bs001.html#overview-of-week-8" style="font-size: 80%;">Overview of week 8</a></li>
<!-- navigation toc: --> <li><a href="._week6-bs001.html#overview" style="font-size: 80%;">Overview</a></li>
<!-- navigation toc: --> <li><a href="._week6-bs002.html#brief-reminder-on-newton-raphson-s-method" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
<!-- navigation toc: --> <li><a href="._week6-bs003.html#the-equations" style="font-size: 80%;">The equations</a></li>
<!-- navigation toc: --> <li><a href="._week6-bs004.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
Expand All @@ -211,32 +212,33 @@
<!-- navigation toc: --> <li><a href="._week6-bs018.html#steepest-descent-method" style="font-size: 80%;">Steepest descent method</a></li>
<!-- navigation toc: --> <li><a href="._week6-bs018.html#steepest-descent-method" style="font-size: 80%;">Steepest descent method</a></li>
<!-- navigation toc: --> <li><a href="._week6-bs019.html#final-expressions" style="font-size: 80%;">Final expressions</a></li>
<!-- navigation toc: --> <li><a href="._week6-bs020.html#code-examples-for-steepest-descent" style="font-size: 80%;">Code examples for steepest descent</a></li>
<!-- navigation toc: --> <li><a href="._week6-bs021.html#simple-codes-for-steepest-descent-and-conjugate-gradient-using-a-2-times-2-matrix-in-c-python-code-to-come" style="font-size: 80%;">Simple codes for steepest descent and conjugate gradient using a \( 2\times 2 \) matrix, in c++, Python code to come</a></li>
<!-- navigation toc: --> <li><a href="._week6-bs022.html#the-routine-for-the-steepest-descent-method" style="font-size: 80%;">The routine for the steepest descent method</a></li>
<!-- navigation toc: --> <li><a href="._week6-bs023.html#steepest-descent-example" style="font-size: 80%;">Steepest descent example</a></li>
<!-- navigation toc: --> <li><a href="._week6-bs031.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
<!-- navigation toc: --> <li><a href="._week6-bs031.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
<!-- navigation toc: --> <li><a href="._week6-bs031.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
<!-- navigation toc: --> <li><a href="._week6-bs031.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
<!-- navigation toc: --> <li><a href="._week6-bs028.html#conjugate-gradient-method-and-iterations" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
<!-- navigation toc: --> <li><a href="._week6-bs031.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
<!-- navigation toc: --> <li><a href="._week6-bs031.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
<!-- navigation toc: --> <li><a href="._week6-bs031.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
<!-- navigation toc: --> <li><a href="._week6-bs032.html#simple-implementation-of-the-conjugate-gradient-algorithm" style="font-size: 80%;">Simple implementation of the Conjugate gradient algorithm</a></li>
<!-- navigation toc: --> <li><a href="._week6-bs033.html#broyden-fletcher-goldfarb-shanno-algorithm" style="font-size: 80%;">Broyden–Fletcher–Goldfarb–Shanno algorithm</a></li>
<!-- navigation toc: --> <li><a href="._week6-bs034.html#stochastic-gradient-descent" style="font-size: 80%;">Stochastic Gradient Descent</a></li>
<!-- navigation toc: --> <li><a href="._week6-bs035.html#computation-of-gradients" style="font-size: 80%;">Computation of gradients</a></li>
<!-- navigation toc: --> <li><a href="._week6-bs036.html#sgd-example" style="font-size: 80%;">SGD example</a></li>
<!-- navigation toc: --> <li><a href="._week6-bs037.html#the-gradient-step" style="font-size: 80%;">The gradient step</a></li>
<!-- navigation toc: --> <li><a href="._week6-bs038.html#simple-example-code" style="font-size: 80%;">Simple example code</a></li>
<!-- navigation toc: --> <li><a href="._week6-bs039.html#when-do-we-stop" style="font-size: 80%;">When do we stop?</a></li>
<!-- navigation toc: --> <li><a href="._week6-bs040.html#slightly-different-approach" style="font-size: 80%;">Slightly different approach</a></li>
<!-- navigation toc: --> <li><a href="._week6-bs041.html#program-for-stochastic-gradient" style="font-size: 80%;">Program for stochastic gradient</a></li>
<!-- navigation toc: --> <li><a href="._week6-bs042.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
<!-- navigation toc: --> <li><a href="._week6-bs043.html#codes-from-numerical-recipes" style="font-size: 80%;">Codes from numerical recipes</a></li>
<!-- navigation toc: --> <li><a href="._week6-bs044.html#finding-the-minimum-of-the-harmonic-oscillator-model-in-one-dimension" style="font-size: 80%;">Finding the minimum of the harmonic oscillator model in one dimension</a></li>
<!-- navigation toc: --> <li><a href="._week6-bs045.html#functions-to-observe" style="font-size: 80%;">Functions to observe</a></li>
<!-- navigation toc: --> <li><a href="._week6-bs020.html#our-simple-2-times-2-example" style="font-size: 80%;">Our simple \( 2\times 2 \) example</a></li>
<!-- navigation toc: --> <li><a href="._week6-bs021.html#derivatives-and-more" style="font-size: 80%;">Derivatives and more</a></li>
<!-- navigation toc: --> <li><a href="._week6-bs022.html#simple-codes-for-steepest-descent-and-conjugate-gradient-using-a-2-times-2-matrix-in-c-python-code-to-come" style="font-size: 80%;">Simple codes for steepest descent and conjugate gradient using a \( 2\times 2 \) matrix, in c++, Python code to come</a></li>
<!-- navigation toc: --> <li><a href="._week6-bs023.html#the-routine-for-the-steepest-descent-method" style="font-size: 80%;">The routine for the steepest descent method</a></li>
<!-- navigation toc: --> <li><a href="._week6-bs024.html#steepest-descent-example" style="font-size: 80%;">Steepest descent example</a></li>
<!-- navigation toc: --> <li><a href="._week6-bs032.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
<!-- navigation toc: --> <li><a href="._week6-bs032.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
<!-- navigation toc: --> <li><a href="._week6-bs032.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
<!-- navigation toc: --> <li><a href="._week6-bs032.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
<!-- navigation toc: --> <li><a href="._week6-bs029.html#conjugate-gradient-method-and-iterations" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
<!-- navigation toc: --> <li><a href="._week6-bs032.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
<!-- navigation toc: --> <li><a href="._week6-bs032.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
<!-- navigation toc: --> <li><a href="._week6-bs032.html#conjugate-gradient-method" style="font-size: 80%;">Conjugate gradient method</a></li>
<!-- navigation toc: --> <li><a href="._week6-bs033.html#simple-implementation-of-the-conjugate-gradient-algorithm" style="font-size: 80%;">Simple implementation of the Conjugate gradient algorithm</a></li>
<!-- navigation toc: --> <li><a href="._week6-bs034.html#broyden-fletcher-goldfarb-shanno-algorithm" style="font-size: 80%;">Broyden–Fletcher–Goldfarb–Shanno algorithm</a></li>
<!-- navigation toc: --> <li><a href="._week6-bs035.html#stochastic-gradient-descent" style="font-size: 80%;">Stochastic Gradient Descent</a></li>
<!-- navigation toc: --> <li><a href="._week6-bs036.html#computation-of-gradients" style="font-size: 80%;">Computation of gradients</a></li>
<!-- navigation toc: --> <li><a href="._week6-bs037.html#sgd-example" style="font-size: 80%;">SGD example</a></li>
<!-- navigation toc: --> <li><a href="._week6-bs038.html#the-gradient-step" style="font-size: 80%;">The gradient step</a></li>
<!-- navigation toc: --> <li><a href="._week6-bs039.html#simple-example-code" style="font-size: 80%;">Simple example code</a></li>
<!-- navigation toc: --> <li><a href="._week6-bs040.html#when-do-we-stop" style="font-size: 80%;">When do we stop?</a></li>
<!-- navigation toc: --> <li><a href="._week6-bs041.html#slightly-different-approach" style="font-size: 80%;">Slightly different approach</a></li>
<!-- navigation toc: --> <li><a href="._week6-bs042.html#program-for-stochastic-gradient" style="font-size: 80%;">Program for stochastic gradient</a></li>
<!-- navigation toc: --> <li><a href="._week6-bs043.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
<!-- navigation toc: --> <li><a href="._week6-bs044.html#codes-from-numerical-recipes" style="font-size: 80%;">Codes from numerical recipes</a></li>
<!-- navigation toc: --> <li><a href="._week6-bs045.html#finding-the-minimum-of-the-harmonic-oscillator-model-in-one-dimension" style="font-size: 80%;">Finding the minimum of the harmonic oscillator model in one dimension</a></li>
<!-- navigation toc: --> <li><a href="._week6-bs046.html#functions-to-observe" style="font-size: 80%;">Functions to observe</a></li>

</ul>
</li>
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</center>
<br>
<center>
<h4>Jan 1, 2024</h4>
<h4>February 23, 2024</h4>
</center> <!-- date -->
<br>

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<li><a href="._week6-bs008.html">9</a></li>
<li><a href="._week6-bs009.html">10</a></li>
<li><a href="">...</a></li>
<li><a href="._week6-bs045.html">46</a></li>
<li><a href="._week6-bs046.html">47</a></li>
<li><a href="._week6-bs001.html">&raquo;</a></li>
</ul>
<!-- ------------------- end of main content --------------- -->
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