x N ∗ = c N / u N , N {\displaystyle \displaystyle x_{N}^{*}\,=\,c_{N}/u_{N,N}} ;
for (i = N-1; i >= 1; i--)
x i ∗ := ( c i − ∑ j = i + 1 N u i , j x j ∗ ) / u i , i {\displaystyle \displaystyle x_{i}^{*}\,:=\,\left(c_{i}\,-\,\sum _{j=i+1}^{N}u_{i,j}x_{j}^{*}\right)/u_{i,i}} ;
;
;