Exercise 2.5.43 (Elimination for a block matrix)

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The block pivots are $A$ and $S = D - C A^{- 1} B$ (and $d - cb ∕ a$ is the correct second pivot of an ordinary 2 by 2 matrix). The example problem has Schur complement

S = [\begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix}] - [\begin{matrix} 4 \\ 4 \end{matrix}] \frac{1}{2} [\begin{matrix} 3 & 3 \end{matrix}] = [\begin{matrix} - 5 & - 6 \\ - 6 & - 5 \end{matrix}] .

mathchakra

2021-12-19 17:44

Exercise 2.5.43 (Elimination for a block matrix)

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