A New Preconditioned Gauss-Seidel Method faster than the Classical Gauss-Seidel Method

In this paper, we present a new preconditioned Gauss-Seidel (GS) method for solving the linear system 𝐴𝑥 = 𝑏 and compared the proposed method with the standard Gauss-Seidel method. We produced some comparison theorems to show the efficiency of the proposed method. Numerical examples are also being studied to know the rate of convergence, memory requirements and time to converge. Finally, the numerical experiments show that the proposed method is better than the standard Gauss-Seidel method, the preconditioned GS methods with the preconditioners such as 𝐼 + 𝐶 6 , 𝐼 + 𝑃1 8 and 𝐼 + 𝑃2 8 .