LU分解
a 11 = u 11 a 12 = u 12 a 21 = l 21 u 11 a 22 = l 21 u 12 + u 22 {\displaystyle {\begin{aligned}a_{11}&=u_{11}\\a_{12}&=u_{12}\\a_{21}&=l_{21}u_{11}\\a_{22}&=l_{21}u_{12}+u_{22}\end{aligned}}}
上式を上から順に解くことでL , U が求められる。 L = [ 1 0 a 21 a 11 1 ] U = [ a 11 a 12 0 a 22 − a 21 a 12 a 11 ] {\displaystyle {\begin{aligned}L&={\begin{bmatrix}1&0\\{\frac {a_{21}}{a_{11}}}&1\end{bmatrix}}\\U&={\begin{bmatrix}a_{11}&a_{12}\\0&a_{22}-{\frac {a_{21}a_{12}}{a_{11}}}\end{bmatrix}}\end{aligned}}}