Consider the iterative solution of a linear system Ax = b of size n x n...

  

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Consider the iterative solution of a linear system Ax = b of size n x n by iterative method based on a splitting of the matrix A = D + E and the iteration: xk+1 D-16-D Exk. == For the choice D = diag(A) (diagonal part of A) we get the Jacobi iteration, and for the choice D = udiag(A) (upper-triangular part of A) we get the Gauss-Seidel iteration. Consider the matrix A 20 -10 6 0 -10 20 3 1 A = 6 3 14 3 0 1 3 4 Use MATLAB to compute the iteration matrices B = -D-E corresponding to this A for the Jacobi iteration, BJacobi, and Gauss-Seidel iteration, BGS. BJacobi Act Go BGS = Enter your answer here Define what we mean by the spectral norm of a matrix B. Answer: Enter your answer here What are the corresponding values of the spectral norms p(BJacobi) and p(BGS)? p(BJacobi) = Enter your answer here p(BGS) = Enter your answer here What does this imply about the convergence of the two iterative methods? Consider the iterative solution of a linear system Ax = b of size n x n by iterative method based on a splitting of the matrix A = D + E and the iteration: xk+1 D-16-D Exk. == For the choice D = diag(A) (diagonal part of A) we get the Jacobi iteration, and for the choice D = udiag(A) (upper-triangular part of A) we get the Gauss-Seidel iteration. Consider the matrix A 20 -10 6 0 -10 20 3 1 A = 6 3 14 3 0 1 3 4 Use MATLAB to compute the iteration matrices B = -D-E corresponding to this A for the Jacobi iteration, BJacobi, and Gauss-Seidel iteration, BGS. BJacobi Act Go BGS = Enter your answer here Define what we mean by the spectral norm of a matrix B. Answer: Enter your answer here What are the corresponding values of the spectral norms p(BJacobi) and p(BGS)? p(BJacobi) = Enter your answer here p(BGS) = Enter your answer here What does this imply about the convergence of the two iterative methods?