From 77a16d71f2c9d3e5c8e0cdfb3e1225cba4f11775 Mon Sep 17 00:00:00 2001 From: flavis Date: Wed, 20 May 2020 11:22:14 +0200 Subject: [PATCH] update num and theo --- sose2020/ana/lectures | 2 +- sose2020/num/uebungen/num3.pdf | Bin 112440 -> 112837 bytes sose2020/num/uebungen/num3.tex | 18 ++++++++++---- sose2020/theo/uebungen/theo5.pdf | Bin 113252 -> 117429 bytes sose2020/theo/uebungen/theo5.tex | 41 +++++++++++++++++++++++++------ 5 files changed, 47 insertions(+), 14 deletions(-) diff --git a/sose2020/ana/lectures b/sose2020/ana/lectures index 7035188..e4c6c9e 160000 --- a/sose2020/ana/lectures +++ b/sose2020/ana/lectures @@ -1 +1 @@ -Subproject commit 7035188af95eef3fdd7dd248590d2eec53fdaa3d +Subproject commit e4c6c9e0fa273d01d3250ca571f25334e6b87849 diff --git a/sose2020/num/uebungen/num3.pdf b/sose2020/num/uebungen/num3.pdf index a41bad56960c6e07e28a6791ca192ea684bb498f..ed4fa627c67cd0b57beb3776c99bdcf00fc6fc9a 100644 GIT binary patch delta 15534 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\Vert_2 \\ &\Vert x \Vert_2 = \sqrt{\sum_{k=1}^{n} |x_k|^2} \ge \sqrt{\Vert x \Vert_{\infty}^2} = \Vert x \Vert_{\infty} .\end{align*} Damit folgt \begin{align*} - &\Vert x \Vert_2 \le \Vert x \Vert_1 \le \sqrt{n} \Vert x \Vert_2 \\ - &\Vert x \Vert_\infty \le \Vert x \Vert_2 \le \sqrt{n} \Vert x \Vert_\infty + \frac{1}{\sqrt{n}} \Vert x \Vert_1 \le &\Vert x \Vert_2 \le \Vert x \Vert_1 \\ + \frac{1}{\sqrt{n}} \Vert x \Vert_1 \le &\Vert x \Vert_{\infty} \le \Vert x \Vert_1 \\ + \Vert x \Vert_2 \le &\Vert x \Vert_1 \le \sqrt{n} \Vert x \Vert_2 \\ + \frac{1}{\sqrt{n}} \Vert x \Vert_2 \le &\Vert x \Vert_{\infty} \le \Vert x \Vert_2 \\ + \Vert x \Vert_\infty \le \Vert x \Vert_2 \le &\Vert x \Vert_1 \le \sqrt{n} \Vert x \Vert_2 + \le n \Vert x \Vert_\infty \\ + \Vert x \Vert_\infty \le &\Vert x \Vert_2 \le \sqrt{n} \Vert x \Vert_\infty .\end{align*} - Die anderen Kombinationen folgen durch Multiplikation mit $\frac{1}{\sqrt{n}}$. - Für $n \to \infty$ ist $\sqrt{n} \to \infty$. + Für $n = 1$ sind alle Abschätzungen scharf, denn dann ist + $\Vert x \Vert_1 = \Vert x \Vert_2 = \Vert x \Vert_{\infty}$ und $\sqrt{n} = \frac{1}{\sqrt{n}} = 1$. + + Es gilt $n \xrightarrow{n \to \infty} \infty$, $\sqrt{n} \xrightarrow{n \to \infty} \infty$ und + $\frac{1}{\sqrt{n}} \xrightarrow{n \to \infty} 0$. \end{enumerate} \end{aufgabe} diff --git a/sose2020/theo/uebungen/theo5.pdf b/sose2020/theo/uebungen/theo5.pdf index 20d50ab5b44a90df840313a9e060391a24721753..e3497a4adfe3e74bd05c0568e6b0b23c2f150467 100644 GIT binary patch delta 68432 zcmZsiV{j!*w63#bV`AI3or!JRwv!#(JLY6!+s4GU?POw3biZ?M-GBFA*XpXSu3m4i zuIKGqM~~1gX)sCT5NzDMph5;3;If`hBK{~^;I0vCgrW4X{YwBWDk?7@gA_EzUvNM* zXGk(nc3u?0h5&;U%Gcitp_4Ncw=n~@=!fPb`KHRQ&WozLO257ipZ5s!;}du*i-@KS zt=%2{fQOK%DH8IEDMum8TryF11spP23+{)j?W2=gZ3U~ihViQNxQp>B;ON&TquIx2 zEfe<*_M7Kr0UQo#78NR3ax&~s z`O+{+)%fUs+_WfVLJEp%U_~+)o7w`&L>Bky;`S&T@P3V+y{!XyuSPN7~>R<$g* zWn#Qnb`a7Odtn^uz>m*HtSklANV;qw>gwG5osTwI+CY-p0_R*XPoPkZW|+9PsZLdA 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