Consider an n x n tridiagonal matrix of the form Ta a -1 -1 -1 -1...

 

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Consider an n x n tridiagonal matrix of the form Ta a -1 -1 -1 -1 -1 -1 -1 a -1 -1 -1 where a is a real parameter. Now take a = 2: (i). Will the Jacobi iteration converge for this matrix? If so, what will its con- vergence factor be? (ii). Will the Gauss-Seidel iteration converge for this matrix? If so, what will its convergence factor be? (iii). For which values of w will the SOR iteration converge? Consider an n x n tridiagonal matrix of the form Ta a -1 -1 -1 -1 -1 -1 -1 a -1 -1 -1 where a is a real parameter. Now take a = 2: (i). Will the Jacobi iteration converge for this matrix? If so, what will its con- vergence factor be? (ii). Will the Gauss-Seidel iteration converge for this matrix? If so, what will its convergence factor be? (iii). For which values of w will the SOR iteration converge?