# Gauss–Seidel method

Iterative method used to solve a linear system of equations / From Wikipedia, the free encyclopedia

In numerical linear algebra, the **Gauss–Seidel method**, also known as the **Liebmann method** or the **method of successive displacement**, is an iterative method used to solve a system of linear equations. It is named after the German mathematicians Carl Friedrich Gauss and Philipp Ludwig von Seidel, and is similar to the Jacobi method. Though it can be applied to any matrix with non-zero elements on the diagonals, convergence is only guaranteed if the matrix is either strictly diagonally dominant,[1] or symmetric and positive definite. It was only mentioned in a private letter from Gauss to his student Gerling in 1823.[2] A publication was not delivered before 1874 by Seidel.[3]