Our 4×4 matrix problem x(k+1)1=(b1−a12x(k)2−a13x(k)3−a14x(k)4)/a11x(k+1)2=(b2−a21x(k)1−a23x(k)3−a24x(k)4)/a22x(k+1)3=(b3−a31x(k)1−a32x(k)2−a34x(k)4)/a33x(k+1)4=(b4−a41x(k)1−a42x(k)2−a43x(k)3)/a44, can be rewritten as x(k+1)1=(b1−a12x(k)2−a13x(k)3−a14x(k)4)/a11x(k+1)2=(b2−a21x(k+1)1−a23x(k)3−a24x(k)4)/a22x(k+1)3=(b3−a31x(k+1)1−a32x(k+1)2−a34x(k)4)/a33x(k+1)4=(b4−a41x(k+1)1−a42x(k+1)2−a43x(k+1)3)/a44, which allows us to utilize the preceding solution (forward substitution). This improves normally the convergence behavior and leads to the Gauss-Seidel method!