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Merge pull request #24 from steohan/patch-1

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Fehlerhafte Berechnung von l_22 behoben.
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Martin Thoma 2013-09-18 13:59:42 -07:00
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documents/Numerik/Klausur1/Aufgabe1.tex
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@ -124,7 +124,7 @@ Falls $A$ symmetrisch ist, gilt:
l_{11} &= \sqrt{a_{11}} = 3\\
l_{21} &= \frac{a_{21}}{l_{11}} = \frac{4}{3}\\
l_{31} &= \frac{a_{31}}{l_{11}} = \frac{12}{3} = 4\\
l_{22} &= \sqrt{a_{21} - {l_{21}}^2} = \sqrt{\frac{4}{3} - \frac{16}{9}}= \sqrt{-\frac{4}{9}} \notin \mathbb{R}\\
l_{22} &= \sqrt{a_{22} - {l_{21}}^2} = \sqrt{1 - \frac{16}{9}}= \sqrt{-\frac{7}{9}} \notin \mathbb{R}\\
& \Rightarrow \text{Es ex. keine Cholesky-Zerlegung, aber $A$ ist symmetrisch}\\
& \Rightarrow \text{$A$ ist nicht pos. Definit}
\end{align}