A technique for solving a set of n linear equations in n unknowns. If the system is summarized by Ax = b, then taking initial values as $x_i^{\left(1\right)}=\frac{b_i}{a_{ii}}$, it uses the iterative relation $x_i^{\left(k\right)}=\frac{b_i-{\displaystyle \sum _{j<i}{a}_{ij}{x}_j^{\left(k\right)}}-{\displaystyle \sum _{j>i}{a}_{ij}{x}_j^{\left(k-1\right)}}}{a_{ii}}$, so it uses the new values immediately they are available, unlike the Jacobi method.