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\)
Mục 2.11 Phân Tích \(A = LU\)
Mục Tiêu
Tiểu Mục 2.11.1 Phân rã \(A = LU\) trong lập trình
Output 2.11.1.
\begin{equation*}
\bmat{1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \\ 10 & 11 & 12} = \bmat{1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1} \cdot \bmat{1 & 0 & 0 & 0 \\ 4 & 1 & 0 & 0 \\ 7 & 2 & 1 & 0 \\ 10 & 3 & 0 & 1} \cdot \bmat{1 & 2 & 3 \\ 0 & -3 & -6 \\ 0 & 0 & 0 \\ 0 & 0 & 0}
\end{equation*}
Output 2.11.2.
\begin{equation*}
\bmat{1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \\ 10 & 11 & 12} = \bmat{0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 1 \\ 0 & 0 & 1 & 0 \\ 1 & 0 & 0 & 0} \cdot \bmat{1 & 0 & 0 & 0 \\ \frac{1}{10} & 1 & 0 & 0 \\ \frac{7}{10} & \frac{1}{3} & 1 & 0 \\ \frac{2}{5} & \frac{2}{3} & 0 & 1} \cdot \bmat{10 & 11 & 12 \\ 0 & \frac{9}{10} & \frac{9}{5} \\ 0 & 0 & 0 \\ 0 & 0 & 0}
\end{equation*}
