Question: The matrix A = arises in the finite difference (and finite element) discretization of the Poisson equation on a nine point square grid. Solve the

The matrix
A =

arises in the finite difference (and finite element) discretization of the Poisson equation on a nine point square grid. Solve the linear system A u = e5 using
(a) Gaussian Elimination
(b) Jacobi iteration
(c) Gauss-Seidel iteration
(d) SOR based on the Jacobi spectral radius

() 0 0 0 0 1 14 000010141 000100410 001014001 010-41010 100410-00 014001000 141010000 410100000

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a u 0625 125 0625 125 375 125 0625 125 0625 T b It takes 11 Jacobi iterations to compute the ... View full answer

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