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31 Consider the iterative solution of a linear system Ax = b of size n x n by iterative method based on a splitting of

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31

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 -10 20 3 A= 6 3 14 3 0 1 3 4 6 0 1 Use MATLAB to compute the iteration matrices B = - D-1 E corresponding to this A for the Jacobi iteration, B Jacobi, and Gauss-Seidel iteration, BGS. BJacobi = Enter your answer here BGS = Enter your answer here Define what we mean by the spectral norm of a matrix B

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