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notes/notes.org
@@ -1855,7 +1855,7 @@ Consider factorization of \(\begin{bmatrix}\epsilon & 1 \\1 & 1
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\(L = \begin{bmatrix}1 & 0 \\1/\epsilon & 1 \end{bmatrix}\),
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\(U = \begin{bmatrix}\epsilon & 1 \\0 & 1-1/\epsilon \end{bmatrix}\)
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- Rounding: \(\fl(U) = \begin{bmatrix}\epsilon & 1 \\0 & -1/\epsilon \end{bmatrix}\)
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-- This leads to \(L\fl(U)) = \begin{bmatrix}\epsilon & 1 \\1 & 0 \end{bmatrix}\), a backward error of \(\begin{bmatrix}0 & 0 \\0 & 1 \end{bmatrix}\)
+- This leads to \(L\fl(U) = \begin{bmatrix}\epsilon & 1 \\1 & 0 \end{bmatrix}\), a backward error of \(\begin{bmatrix}0 & 0 \\0 & 1 \end{bmatrix}\)
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#+LATEX: \end{hidden}
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*** Round-off Error in LU with Pivoting
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