fixes to convergence result, tweak

berkeley-stat243 · Nov 8, 2023 · cec3b15 · cec3b15
1 parent 3d2535f
commit cec3b15
Show file tree

Hide file tree

Showing 13 changed files with 5 additions and 5 deletions.
diff --git a/_freeze/units/unit11-optim/execute-results/html.json b/_freeze/units/unit11-optim/execute-results/html.json
diff --git a/_freeze/units/unit11-optim/execute-results/tex.json b/_freeze/units/unit11-optim/execute-results/tex.json
diff --git a/_freeze/units/unit11-optim/figure-pdf/cell-12-output-2.pdf b/_freeze/units/unit11-optim/figure-pdf/cell-12-output-2.pdf
diff --git a/_freeze/units/unit11-optim/figure-pdf/cell-2-output-1.pdf b/_freeze/units/unit11-optim/figure-pdf/cell-2-output-1.pdf
diff --git a/_freeze/units/unit11-optim/figure-pdf/cell-2-output-2.pdf b/_freeze/units/unit11-optim/figure-pdf/cell-2-output-2.pdf
diff --git a/_freeze/units/unit11-optim/figure-pdf/cell-2-output-4.pdf b/_freeze/units/unit11-optim/figure-pdf/cell-2-output-4.pdf
diff --git a/_freeze/units/unit11-optim/figure-pdf/cell-3-output-1.pdf b/_freeze/units/unit11-optim/figure-pdf/cell-3-output-1.pdf
diff --git a/_freeze/units/unit11-optim/figure-pdf/cell-4-output-1.pdf b/_freeze/units/unit11-optim/figure-pdf/cell-4-output-1.pdf
diff --git a/_freeze/units/unit11-optim/figure-pdf/cell-7-output-1.pdf b/_freeze/units/unit11-optim/figure-pdf/cell-7-output-1.pdf
diff --git a/_freeze/units/unit11-optim/figure-pdf/cell-7-output-2.pdf b/_freeze/units/unit11-optim/figure-pdf/cell-7-output-2.pdf
diff --git a/_freeze/units/unit11-optim/figure-pdf/cell-8-output-1.pdf b/_freeze/units/unit11-optim/figure-pdf/cell-8-output-1.pdf
diff --git a/_freeze/units/unit11-optim/figure-pdf/cell-9-output-1.pdf b/_freeze/units/unit11-optim/figure-pdf/cell-9-output-1.pdf
diff --git a/units/unit11-optim.qmd b/units/unit11-optim.qmd
@@ -611,7 +611,7 @@ for some $\xi_{t}\in[x^{*},x_{t}]$. Making use of the N-R update
 equation:
 $x_{t+1}=x_{t}-\frac{f^{\prime}(x_{t})}{f^{\prime\prime}(x_{t})}$ to
 substitute , and some algebra, we have
-$$\frac{|x^{*}-x_{t+1}|}{(x^{*}-x_{t})^{2}}=\left| \frac{1}{2}\frac{f^{\prime\prime\prime}(\xi_{t})}{f^{\prime\prime}(x_{t})} \right|.$$
+$$\frac{|\epsilon_{t+1}|}{|\epsilon_t|^{\beta}} = \frac{|x^{*}-x_{t+1}|}{(x^{*}-x_{t})^{2}}=\left| \frac{1}{2}\frac{f^{\prime\prime\prime}(\xi_{t})}{f^{\prime\prime}(x_{t})} \right|.$$
 If the limit of the ratio on the right hand side exists (note the assumption of twice continuous differentiability) and is equal to
 $c$:
 $$c=\lim_{x_{t}\to x^{*}}\left|\frac{1}{2}\frac{f^{\prime\prime\prime}(\xi_{t})}{f^{\prime\prime}(x_{t})}\right|=\left|\frac{1}{2}\frac{f^{\prime\prime\prime}(x^{*})}{f^{\prime\prime}(x^{*})}\right|$$