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\begin{document}


Aufgabe 125

Gegeben sei das eindeutig l\"{o}sbare lineare Gleichungssystem $\ A\cdot 
\overrightarrow{x}=\overrightarrow{b}$ mit 

$A=\left( 
\begin{array}{cccccc}
4 & -1 & 0 & -1 & 0 & 0 \\ 
-1 & 4 & -1 & 0 & -1 & 0 \\ 
0 & -1 & 4 & 0 & 0 & -1 \\ 
-1 & 0 & 0 & 4 & -1 & 0 \\ 
0 & -1 & 0 & -1 & 4 & -1 \\ 
0 & 0 & -1 & 0 & -1 & 4%
\end{array}%
\right) $, $\overrightarrow{b}=\left( 
\begin{array}{c}
2 \\ 
1 \\ 
2 \\ 
2 \\ 
1 \\ 
2%
\end{array}%
\right) $

a.\qquad Sei $\overrightarrow{x}^{\left( 0\right) }=\overrightarrow{0}$.
Berechnen Sie die N\"{a}herungsl\"{o}sung $\overrightarrow{x}^{\left(
3\right) }$\ des Systems, die man nach 3 Schritten des
Gesamtschrittverfahrens erh\"{a}lt.

b.

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