The beauty of this method, is if a matrix with diagonal dominance or is symmetric and positive definite, as well as an initial guess for the x values it is guaranteed to converge (it often converges even if these conditions are not met). Įxtracting the pure technical information, the Gauss-Seidel Method is an iterative method, where given Ax = b and A and b are known, we can determine the x values.
Though it can be applied to any matrix with non-zero elements on the diagonals, convergence is only guaranteed if the matrix is either diagonally dominant, or symmetric and positive definite. It is named after the German mathematicians Carl Friedrich Gauss and Philipp Ludwig von Seidel, and is similar to the Jacobi method. Also known as the Liebmann method or the method of successive displacement, is an iterative method used to solve a linear system of equations.