Do 5 steps, starting from x₀ = [1    1    1]. Compare with the Gauss–Seidel iteration. Which of the two seems to converge faster? Show the details of your work.

Show convergence in Prob. 16 by verifying that I - A,
where A is the matrix in Prob. 16 with the rows divided by the corresponding main diagonal entries, has the eigenvalues -0.519589 and 0.259795 ± 0.246603i.

Data from Prob. 16

Do 5 steps, starting from x₀ = [1    1    1]. Compare with the Gauss–Seidel iteration. Which of the two seems to converge faster? Show the details of your work.

The system in Prob. 10

Data from Prob. 10

Do 5 steps, starting from x₀ = [1    1    1]^T and using 6S in the computation. Make sure that you solve each equation for the variable that has the largest coefficient (why?). Show the details.

4x₁           + 5x₃ = 12.5
  x₁ + 6x₂ + 2x₃ = 18.5
8x₁ + 2x₂ +  x₃ = -11.5