Question
The system of equations Az = b can also be solved using an iterative scheme. One such scheme for a square matrix A is
The system of equations Az = b can also be solved using an iterative scheme. One such scheme for a square matrix A is the Jacobi method in which successive approximations are generated by Xk+1= D-b-D-k where is the k-th approximation, and A = D + A with D being a diagonal matrix whose entries are the respective diagonal entries of A, and A-D. Show how the iteration scheme may be derived. Under what condition does the scheme converge for any initial approximation To ? Using the fact that the roots of the equation 1 (3/4)A (7/36): satisfy | < 1, does the scheme converge for the A matrix of part (a)? Explain your answer.
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