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Aufgaben/Aufg125swp.tex

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+\documentclass{article}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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+%TCIDATA{BibliographyScheme=Manual}
+%TCIDATA{Created=Saturday, December 30, 2006 12:55:45}
+%TCIDATA{LastRevised=Saturday, December 30, 2006 13:08:01}
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+
+\newtheorem{theorem}{Theorem}
+\newtheorem{acknowledgement}[theorem]{Acknowledgement}
+\newtheorem{algorithm}[theorem]{Algorithm}
+\newtheorem{axiom}[theorem]{Axiom}
+\newtheorem{case}[theorem]{Case}
+\newtheorem{claim}[theorem]{Claim}
+\newtheorem{conclusion}[theorem]{Conclusion}
+\newtheorem{condition}[theorem]{Condition}
+\newtheorem{conjecture}[theorem]{Conjecture}
+\newtheorem{corollary}[theorem]{Corollary}
+\newtheorem{criterion}[theorem]{Criterion}
+\newtheorem{definition}[theorem]{Definition}
+\newtheorem{example}[theorem]{Example}
+\newtheorem{exercise}[theorem]{Exercise}
+\newtheorem{lemma}[theorem]{Lemma}
+\newtheorem{notation}[theorem]{Notation}
+\newtheorem{problem}[theorem]{Problem}
+\newtheorem{proposition}[theorem]{Proposition}
+\newtheorem{remark}[theorem]{Remark}
+\newtheorem{solution}[theorem]{Solution}
+\newtheorem{summary}[theorem]{Summary}
+\newenvironment{proof}[1][Proof]{\noindent\textbf{#1.} }{\ \rule{0.5em}{0.5em}}
+\input{tcilatex}
+
+\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.
+
+\end{document}