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 $x_i^{\left(1\right)}=\frac{b_i}{a_{\mathrm{ii}}}$, it uses the iterative relation $x_i^{\left(k\right)}=\frac{b_i-{\sum }_{j\ne i}{a}_{ij}{x}_j^{\left(k-1\right)}}{a_{ii}}$, so it computes a complete set of new values together, unlike the Gauss–Seidel method.