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Computationallinearalgebracourse.pdf

@@ -681,7 +681,7 @@ <h2><span class="section-number">2.6. </span>Householder triangulation<a class="
 done so, you will need to modified
 <a class="reference internal" href="cla_utils.html#cla_utils.exercises3.householder" title="cla_utils.exercises3.householder"><code class="xref py py-func docutils literal notranslate"><span class="pre">cla_utils.exercises3.householder()</span></code></a> to use the <code class="docutils literal notranslate"><span class="pre">kmax</span></code>
 argument. You may make use of the built-in triangular solve
-algorithm <a class="reference external" href="http://scipy.github.io/devdocs/reference/generated/scipy.linalg.solve_triangular.html#scipy.linalg.solve_triangular" title="(in SciPy v1.8.0.dev0+1869.838cfbe)"><code class="xref py py-func docutils literal notranslate"><span class="pre">scipy.linalg.solve_triangular()</span></code></a> (we shall consider
+algorithm <a class="reference external" href="http://scipy.github.io/devdocs/reference/generated/scipy.linalg.solve_triangular.html#scipy.linalg.solve_triangular" title="(in SciPy v1.8.0.dev0+1921.c30fefc)"><code class="xref py py-func docutils literal notranslate"><span class="pre">scipy.linalg.solve_triangular()</span></code></a> (we shall consider
 triangular matrix algorithms briefly later). The test script
 <code class="docutils literal notranslate"><span class="pre">test_exercises3.py</span></code> in the <code class="docutils literal notranslate"><span class="pre">test</span></code> directory will also test this
 function.</p>
@@ -793,7 +793,7 @@ <h2><span class="section-number">2.7. </span>Application: Least squares problems
 appropriate augmented matrix <span class="math notranslate nohighlight">\(\hat{A}\)</span>, calling
 <a class="reference internal" href="cla_utils.html#cla_utils.exercises3.householder" title="cla_utils.exercises3.householder"><code class="xref py py-func docutils literal notranslate"><span class="pre">cla_utils.exercises3.householder()</span></code></a> and extracting appropriate
 subarrays using slice notation, before using
-<a class="reference external" href="http://scipy.github.io/devdocs/reference/generated/scipy.linalg.solve_triangular.html#scipy.linalg.solve_triangular" title="(in SciPy v1.8.0.dev0+1869.838cfbe)"><code class="xref py py-func docutils literal notranslate"><span class="pre">scipy.linalg.solve_triangular()</span></code></a> to solve the resulting upper triangular
+<a class="reference external" href="http://scipy.github.io/devdocs/reference/generated/scipy.linalg.solve_triangular.html#scipy.linalg.solve_triangular" title="(in SciPy v1.8.0.dev0+1921.c30fefc)"><code class="xref py py-func docutils literal notranslate"><span class="pre">scipy.linalg.solve_triangular()</span></code></a> to solve the resulting upper triangular
 system, before returning the solution <span class="math notranslate nohighlight">\(x\)</span>. The test script
 <code class="docutils literal notranslate"><span class="pre">test_exercises3.py</span></code> in the <code class="docutils literal notranslate"><span class="pre">test</span></code> directory will also test this
 function.</p>

L2_QR_factorisation.html

@@ -114,7 +114,7 @@ <h2><span class="section-number">3.2. </span>Operation count for modified Gram-S
 <blockquote>
 <div><div class="math notranslate nohighlight">
 \[N_{\mbox{FLOPS}} \sim \sum_{i=1}^n \sum_{j=i+1}^n 4m
-\sim 4m \int_0^n \int_{x}^n x'\,d x' \,d x
+\sim 4m \int_0^n \int_{x}^n \,d x' \,d x
 = 4m\frac{n^2}{2} = 2mn^2,\]</div>
 </div></blockquote>
 <p>as suggested above.</p>

L3_analysing_algorithms.html

@@ -74,7 +74,7 @@ over `j`, which we can estimate by approximating the sum as an integral,
    .. math::
 
       N_{\mbox{FLOPS}} \sim \sum_{i=1}^n \sum_{j=i+1}^n 4m
-      \sim 4m \int_0^n \int_{x}^n x'\,d x' \,d x
+      \sim 4m \int_0^n \int_{x}^n \,d x' \,d x
       = 4m\frac{n^2}{2} = 2mn^2,
 
 as suggested above.