====== LU分解 ======
==== LU decomposition ====

{{tag>..c01}}

　連立一次方程式の係数行列//A//（//n//次元）は下三角行列//L//と上三角行列//U//に三角分解でき，\({u_{kj}} = {a_{kj}} - \sum\limits_{m = 1}^{k - 1} {{l_{km}}{u_{mj}}(j = k,n)} ,{l_{ik}} = ({a_{ik}} - \sum\limits_{m = 1}^{k - 1} {{l_{im}}{u_{mk}})/{u_{kk}}(i = k + 1,n)} \)となる．


~~NOCACHE~~