When very large systems of simultaneous equations require a solution, iterative methods are used. These methods are particularly useful and efficient if
many of the coefficients in the equations are zero, which is often the case in
engineering applications. In this section we shall only describe the Gauss/ Seidel iterative method for solving the n linear non-homogeneous equations:
a11x1a12x2a13x3 . . .a1nxnk1 a21x1a22x2a23x3 . . .a2nxnk2
an1x1an2x2an3x3 . . .annxnkn,
in the n unknowns x1, x2, . . . , xn .