{x}_{k}=\left({a}_{k,n+1}- \sum_{j=k+1}^{n}{a}_{kj}{x}_{j} \right) /{a}_{kk},\:
{{a}_{kj}}^{\left(m+1 \right)}={{a}_{kj}}^{\left(m \right)}/{{a}_{kk}}^{\left(m \right)},
\:{{a}_{ij}}^{\left(m+1 \right)}={{a}_{ij}}^{\left(m \right)}-{{a}_{ik}}^{\left(m \right)}{{a}_{kj}}^{\left(m \right)}.