aboutsummaryrefslogtreecommitdiffstats
path: root/buch/papers/laguerre
diff options
context:
space:
mode:
authorPatrik Müller <patrik.mueller@ost.ch>2022-06-03 07:23:21 +0200
committerPatrik Müller <patrik.mueller@ost.ch>2022-06-03 07:23:21 +0200
commit8fb46098cb8e42a94b8e01ecc809f536d5c7efaf (patch)
tree856162e03079e0d1c560410c9f42cac6682e0ac1 /buch/papers/laguerre
parentAdd n != m to presentation at orthogonality section (diff)
downloadSeminarSpezielleFunktionen-8fb46098cb8e42a94b8e01ecc809f536d5c7efaf.tar.gz
SeminarSpezielleFunktionen-8fb46098cb8e42a94b8e01ecc809f536d5c7efaf.zip
Minor tweaks of presentation
Diffstat (limited to 'buch/papers/laguerre')
-rw-r--r--buch/papers/laguerre/images/rel_error_shifted.pgf4
-rw-r--r--buch/papers/laguerre/images/targets.pdfbin12940 -> 13199 bytes
-rw-r--r--buch/papers/laguerre/presentation/sections/gamma.tex5
-rw-r--r--buch/papers/laguerre/presentation/sections/gamma_approx.tex20
-rw-r--r--buch/papers/laguerre/presentation/sections/laguerre.tex2
-rw-r--r--buch/papers/laguerre/scripts/gamma_approx.py2
6 files changed, 20 insertions, 13 deletions
diff --git a/buch/papers/laguerre/images/rel_error_shifted.pgf b/buch/papers/laguerre/images/rel_error_shifted.pgf
index c11b676..707d492 100644
--- a/buch/papers/laguerre/images/rel_error_shifted.pgf
+++ b/buch/papers/laguerre/images/rel_error_shifted.pgf
@@ -1050,7 +1050,7 @@
\pgfsetbuttcap%
\pgfsetroundjoin%
\pgfsetlinewidth{3.011250pt}%
-\definecolor{currentstroke}{rgb}{0.000000,0.750000,0.750000}%
+\definecolor{currentstroke}{rgb}{0.750000,0.000000,0.750000}%
\pgfsetstrokecolor{currentstroke}%
\pgfsetdash{{3.000000pt}{4.950000pt}}{0.000000pt}%
\pgfpathmoveto{\pgfqpoint{0.712295in}{0.453273in}}%
@@ -1310,7 +1310,7 @@
\pgfsetbuttcap%
\pgfsetroundjoin%
\pgfsetlinewidth{3.011250pt}%
-\definecolor{currentstroke}{rgb}{0.000000,0.750000,0.750000}%
+\definecolor{currentstroke}{rgb}{0.750000,0.000000,0.750000}%
\pgfsetstrokecolor{currentstroke}%
\pgfsetdash{{3.000000pt}{4.950000pt}}{0.000000pt}%
\pgfpathmoveto{\pgfqpoint{5.398422in}{3.760989in}}%
diff --git a/buch/papers/laguerre/images/targets.pdf b/buch/papers/laguerre/images/targets.pdf
index adaeeef..df11068 100644
--- a/buch/papers/laguerre/images/targets.pdf
+++ b/buch/papers/laguerre/images/targets.pdf
Binary files differ
diff --git a/buch/papers/laguerre/presentation/sections/gamma.tex b/buch/papers/laguerre/presentation/sections/gamma.tex
index 37f4a0b..7dca39b 100644
--- a/buch/papers/laguerre/presentation/sections/gamma.tex
+++ b/buch/papers/laguerre/presentation/sections/gamma.tex
@@ -3,8 +3,9 @@
\begin{frame}{Gamma-Funktion}
\begin{columns}
-\begin{column}{0.48\textwidth}
+\begin{column}{0.55\textwidth}
\begin{figure}[h]
+\vspace{-16pt}
\centering
% \scalebox{0.51}{\input{../images/gammaplot.pdf}}
\includegraphics[width=1\textwidth]{../images/gammaplot.pdf}
@@ -12,7 +13,7 @@
\end{figure}
\end{column}
-\begin{column}{0.52\textwidth}
+\begin{column}{0.45\textwidth}
Verallgemeinerung der Fakultät
\begin{align*}
\Gamma(n) = (n-1)!
diff --git a/buch/papers/laguerre/presentation/sections/gamma_approx.tex b/buch/papers/laguerre/presentation/sections/gamma_approx.tex
index 2e4e4e2..4073b3c 100644
--- a/buch/papers/laguerre/presentation/sections/gamma_approx.tex
+++ b/buch/papers/laguerre/presentation/sections/gamma_approx.tex
@@ -48,7 +48,8 @@ R_n(\xi)
\begin{figure}[h]
\centering
-\scalebox{0.91}{\input{../images/rel_error_simple.pgf}}
+% \scalebox{0.91}{\input{../images/rel_error_simple.pgf}}
+\resizebox{!}{0.72\textheight}{\input{../images/rel_error_simple.pgf}}
\caption{Relativer Fehler des einfachen Ansatzes für verschiedene reele Werte
von $z$ und Grade $n$ der Laguerre-Polynome}
\end{figure}
@@ -123,17 +124,22 @@ da Gauss-Quadratur nur für kleine $n$ praktischen Nutzen hat}
\end{frame}
\begin{frame}{Verschiebungsterm}
+\begin{columns}
+\begin{column}{0.625\textwidth}
+\begin{figure}[h]
+\centering
+\includegraphics[width=1\textwidth]{../images/targets.pdf}
+\caption{Optimaler Verschiebungsterm $m^*$ in Abhängigkeit von $z$ und $n$}
+\end{figure}
+\end{column}
+\begin{column}{0.375\textwidth}
\begin{align*}
\Gamma(z)
\approx
\frac{1}{(z-m)_{m}} \sum_{i=1}^{n} x_i^{z + m - 1} A_i
\end{align*}
-
-\begin{figure}[h]
-\centering
-\includegraphics[width=0.5\textwidth]{../images/targets.pdf}
-\caption{Optimaler Verschiebungsterm $m^*$ in Abhängigkeit von $z$ und $n$}
-\end{figure}
+\end{column}
+\end{columns}
\end{frame}
\begin{frame}{Schätzen von $m^*$}
diff --git a/buch/papers/laguerre/presentation/sections/laguerre.tex b/buch/papers/laguerre/presentation/sections/laguerre.tex
index 1add511..07cafb8 100644
--- a/buch/papers/laguerre/presentation/sections/laguerre.tex
+++ b/buch/papers/laguerre/presentation/sections/laguerre.tex
@@ -55,7 +55,7 @@ L_n(x)
\begin{frame}
\begin{figure}[h]
\centering
-\scalebox{0.66}{\input{../images/laguerre_polynomes.pgf}}
+\resizebox{0.74\textwidth}{!}{\input{../images/laguerre_polynomes.pgf}}
\caption{Laguerre-Polynome vom Grad $0$ bis $7$}
\end{figure}
\end{frame}
diff --git a/buch/papers/laguerre/scripts/gamma_approx.py b/buch/papers/laguerre/scripts/gamma_approx.py
index 857c735..53ba76b 100644
--- a/buch/papers/laguerre/scripts/gamma_approx.py
+++ b/buch/papers/laguerre/scripts/gamma_approx.py
@@ -241,7 +241,7 @@ for target in targets:
ax5.semilogy(x, rel_error, label=f"$m={target}$", linewidth=3)
gamma_lgo = eval_laguerre_gamma(x, n=n, func="optimal_shifted")
rel_error = np.abs(calc_rel_error(gamma, gamma_lgo))
-ax5.semilogy(x, rel_error, "c", linestyle="dotted", label="$m^*$", linewidth=3)
+ax5.semilogy(x, rel_error, "m", linestyle="dotted", label="$m^*$", linewidth=3)
ax5.set_xlim(x[0], x[-1])
ax5.set_ylim(5e-9, 5e-8)
ax5.set_xlabel(r"$z$")