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Exercise 2. Explore convergence property of the Jacobi and Jacobi with relaxation (Jacobi_) method for the system A,x = 6 2 - 1 0 0
Exercise 2. Explore convergence property of the Jacobi and Jacobi with relaxation (Jacobi_) method for the system A,x = 6 2 - 1 0 0 - 1 2-1 A, 0 0 b = [1...11 n = 30 : -1 2-1 0 0-1 2 Construct the matrix M for the Jacobi method. Find its maximum and minimum eigen- value. Using these eigenvalues find the optimal relaxation parameter w for the Jacobi method with relaxation. The exact solution x can be found as r =A\6. Implement the method. Starting with the initial guess r(0) = [0000" iterate find approximate solutions until || 2 - |
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