From 143d1a2f7efed062eca357c455def4a49dc0662a Mon Sep 17 00:00:00 2001 From: Martin Thoma Date: Mon, 23 Sep 2013 16:26:16 +0200 Subject: [PATCH] 'Offensichtlich' nun noch offensichtlicher gemacht --- documents/Numerik/UB11/Aufgabe31.tex | 9 ++++++++- documents/Numerik/UB11/UB11.pdf | Bin 125573 -> 126376 bytes 2 files changed, 8 insertions(+), 1 deletion(-) diff --git a/documents/Numerik/UB11/Aufgabe31.tex b/documents/Numerik/UB11/Aufgabe31.tex index 98b0d28..0f509f5 100644 --- a/documents/Numerik/UB11/Aufgabe31.tex +++ b/documents/Numerik/UB11/Aufgabe31.tex @@ -46,7 +46,14 @@ Polynom vom Grad $\leq 2-1 = 1$ sein. Also: \Leftrightarrow c_2 &\stackrel{!}{=} \frac{3a + 5 b}{5 a + 10 b} \end{align} -Offensichtlich gibt es kein $c_2$, dass diese Bedingung für jedes $a,b \in \mathbb{R}$ +Da diese Bedingung für alle $a, b \in \mathbb{R}$ gelten soll, muss +sie auf jeden Fall für $a=1, b=0$ sowie für $a=1, b=1$ gelten. Aber: + +\begin{align} + \frac{2\cdot1+5\cdot0}{5\cdot1+10\cdot0} = \frac{3}{5} &\neq \frac{8}{15} = \frac{3\cdot1+5\cdot1}{5\cdot1+10\cdot1} +\end{align} + +Offensichtlich gibt also es kein $c_2$, dass diese Bedingung für jedes $a,b \in \mathbb{R}$ erfüllt. Daher kann es keine Quadraturformel der Ordnung $5$ mit den Knoten $0$ und $1$ geben. diff --git a/documents/Numerik/UB11/UB11.pdf b/documents/Numerik/UB11/UB11.pdf index 59b5b3d2827d951dca145c281a768230af924310..68766587aaf0151f75c3fa517c2b13e41ce832d4 100644 GIT binary patch delta 26850 zcmZUZQ*fYdux?{p6Wg|J+fHU;+xcQnY}>YNCzFY7PHdik*RE6N;@qvi?5elAo_>3U zE?$Tlq1pBBH}ALEB4pENP+*upq|cs6XT&>H7ae2JVrH zQUa#uc`0qR**~>w0knq_Hh%hjdEG3904o*yu&&H}VajSxn-CpEc65 zpd=aWlx)TsG}T;7H|JF#wU25A_8#SonNO*E1i5gG#!+Yq z=EhSRM&w)=zio09bT4MH=J9b7DU?v>ll#-jP;!Oxp{ZH8^T`+t1@ocHIsc=jS)BQ@ z8>JQR{hUraYF5!0PRiJ zIxbYy^is98{^mlK<0U9rg8|flq|7@W(S;g=*j!AI6W{qO~P_y?3pey$~K10^l#B~h9s|b zV=8_6@+J0++n!fAAp(mrC0e>Pb zFCtN#C&{mLN-^wGdAO;BM#f25ojaXWW53eOiON#4_Z@^->NuM)DpQXBW<+XsHfkRW zUn*N_1xD&0pT_CG^NTI$cb@!nmCt*$Ac3{CtbI9!YqwKO+KfGkUPPM}Jd{#vvtyqJ?glMX-+vl#rZAX1TzrdS}bMZ2?qm8~EMxI;&Q(9)= zdd0YD4FexD)h}&=uAETRYp#`tT!N!2rX(rl%=kZg;jmXvjaD}L(Fl~#vMP>ZFk6a= zjko1NXQP$D?njaGqlilqSu#Z9e}RvyiC>kIQJ)#r>(gj32mDXmKI6>-=fAQ3$y#Bc 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