The Jacobi method is very similar to Gauss-Seidel method. The only difference is that Jacobi method doesn’t use the latest evaluated x_i s in the equation. This method employs a set of old x_i s to determine a set of new x_i s. It means:

The algorithm of this method can be written in the following form:

Step 1: Choose X₀ = [x₀₁,x₀₂,…,x_0n] as a starting point

Step 2: Let

                   

Step 3: : If ||x-x₀||<e  then let X is solution else X₀=X; go to step 2.

Step 5: End.

e: Acceptable approximated error.