diff options
Diffstat (limited to 'buch')
-rw-r--r-- | buch/papers/laguerre/images/rel_error_shifted.pgf | 4 | ||||
-rw-r--r-- | buch/papers/laguerre/images/targets.pdf | bin | 12940 -> 13199 bytes | |||
-rw-r--r-- | buch/papers/laguerre/presentation/sections/gamma.tex | 5 | ||||
-rw-r--r-- | buch/papers/laguerre/presentation/sections/gamma_approx.tex | 20 | ||||
-rw-r--r-- | buch/papers/laguerre/presentation/sections/laguerre.tex | 2 | ||||
-rw-r--r-- | buch/papers/laguerre/scripts/gamma_approx.py | 2 |
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 Binary files differindex adaeeef..df11068 100644 --- a/buch/papers/laguerre/images/targets.pdf +++ b/buch/papers/laguerre/images/targets.pdf 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"$z$") |