1. In MATLAB, A = gallery('poisson', n) returns the block tridiagonal (sparse) matrix A of order n resulting from discretizing Poisson's equation with the

1. In MATLAB, A gallery("poisson', n) returns the block tridiagonal (sparse) matrix A of order n2 resulting from discretizing Poisson's equation with the 5-point operator on an n-by-n mesh. Choose b so that Ax b has solution vector e of all 1's. For n = 20, 30, 40, approximate * 1) by using SOR with optimal w. 2) by using PCG method with the following preconditioner M: .M=1 M = D M = D+L M=(D+L)D-(D+L?) M: incomplete Choleskey factorization of A, (D is the diagonal of A: L is the strict lower triangular part of A) 2. Do the same procedure for Hilbert matrix H of size n= 100, 200. 1. In MATLAB, A gallery("poisson', n) returns the block tridiagonal (sparse) matrix A of order n2 resulting from discretizing Poisson's equation with the 5-point operator on an n-by-n mesh. Choose b so that Ax b has solution vector e of all 1's. For n = 20, 30, 40, approximate * 1) by using SOR with optimal w. 2) by using PCG method with the following preconditioner M: .M=1 M = D M = D+L M=(D+L)D-(D+L?) M: incomplete Choleskey factorization of A, (D is the diagonal of A: L is the strict lower triangular part of A) 2. Do the same procedure for Hilbert matrix H of size n= 100, 200

1. In MATLAB, A = gallery('poisson', n) returns the block tridiagonal (sparse) matrix A of order n resulting from discretizing Poisson's equation with the 5-point operator on an n-by-n mesh. Choose b so that Ar = b has solution vector 2 of all 1's. For n = 20, 30, 40, approximate a 1) by using SOR with optimal w. 2) by using PCG method with the following preconditioner M: M=I M=D M=D+L M = (D+L)D(D+LT) M: incomplete Choleskey factorization of A, (D is the diagonal of A; L is the strict lower triangular part of A) 2. Do the same procedure for Hilbert matrix H of size n = 100, 200.