In this project, we implement the (forward) Gauss-Seidel method and the preconditioned steepest
descent methd (PSD) for solving the linear system Ax = b with A being symmetric positive denite.
The preconditioner in this project is from the Jacobi iterative method: P = D = diag(A). The error
estimator in both iterative methods is the relative residual jjrkjj
jjbjj where rk = b􀀀Axk, and jjbjj is length
of b. We choose the tolerance  = 10􀀀10.

1. Implement the (forward) Gauss-Seidel method for solving Ax = b. Download the matrix A.dat
from Project 2 in Brightspace. Read the matix A (16001600) into your code. Generate b = Axt
with all components of xt being one. Run your code, and output the iteration number k and
relative residual jjrkjj
jjbjj into a le. Plot the relative residual as a function of iteration number. An
example of such plot is Figure 2.4 on Page 128 of the textbook (2nd Edition, attached).
2. Implement the preconditioned steepest descent method. The algorithm: selecting x0, computing
r0 = b 􀀀 Ax0, then: