What is the condition for convergence of Gauss-Seidel method of iteration?

What is the condition for convergence of Gauss-Seidel method of iteration?

The solution of linear equations by iterative methods requires for convergence that the absolute magnitudes of all the eigenvalues of the iteration matrix should be less than unity. The Gauss-Seidel method converges if the number of roots inside the unit circle is equal to the order of the iteration matrix.

How many iterations are performed in Gauss-Seidel method?

20.2 The Gauss-Seidel Iterative Method Begin with x(0) = 0, execute the first two iterations in detail, continue for a total of 12 iterations, and compute the relative residual.

What are the advantages and disadvantages of the Gauss-Seidel iterative method?

Advantages: Faster, more reliable and results are accurate, require less number of iterations; Disadvantages: Program is more complex, memory is more complex.

Which is faster Gauss-Seidel or Newton Raphson?

However the Newton-Raphson method converged faster than the Gauss-Seidel method. The bus voltage magnitudes, angles of each bus along with power generated and consumed at each bus are given in Table 4.4. It can be seen from this table that the total power generated is 174.6 MW whereas the total load is 171 MW.

What are the advantages of Gauss-Seidel method?

Gauss Seidel method is easy to program. Each iteration is relatively fast (computational order is proportional to number of branches and number of buses in the system). Acquires less memory space than NR method.

What is the formula for Gauss Seidel method?

Let’s apply the Gauss-Seidel Method to the system from Example 1: . x1(1) = 3/4 = 0.750. x2(1) = [9 + 2(0.750)] / 6 = 1.750.

When to terminate the iteration in Gauss Seidel?

Terminate the iteration when . Write a function to implement the Gauss-Seidel iteration method, and then solve the same system above, using as the initial guess. Print the error after each iteration. Terminate the iteration when .

When to use successive over relaxation in Gauss-Seidel?

It can be shownthat if matrix is strictly diagonally dominantthen the Gauss-Seidel method converges. The successive over relaxation (SOR)is a method that can be used to speed up the convergence of the iteration. Multiplying a parameter on both sides of the equation we get

How is the Gauss Seidel method similar to the Jacobi method?

The element-wise formula for the Gauss–Seidel method is extremely similar to that of the Jacobi method . The computation of x(k+1) uses the elements of x(k+1) that have already been computed, and only the elements of x(k) that have not been computed in the k+1 iteration.