Gauss–Seidel method is an improved form of Jacobi method, also known as the successive displacement method. This method is named after Carl Friedrich Gauss (Apr. 1777–Feb. 1855) and Philipp Ludwig von Seidel (Oct. 1821–Aug. 1896). The reason the Gauss–Seidel method is commonly known as the successive displacement method is because the second unknown is determined from the first unknown in the current iteration, the third unknown is determined from the first and second unknowns, etc.
Assumption: :

• The system of linear equations to be solved, must have a unique solution.
• There should not be any zeros on the main diagonal of the coefficient matrix A.In case, there exist zeros on its main diagonal, then rows must be interchanged to obtain a coefficient matrix that does not have zero entries on the main diagonal.