Question

4. Set up a verification example using 3x3 system of equations (you may use the system we discussed in class or make up your own). Make sure that you code works correctly. 5. Now solve the above system of equations using Gauss-Seidel iteration, using an initial guess $x_i = 175$ for $i = 1, 2, \dots, N$, setting the iterative convergence criterion and the residual norm criterion to $\epsilon = 10^{-4}$ and $\delta = 10^{-4}$. Find the: a. the solution vector. b. the number of iterations to convergence. c. a plot the residual norm (use the $L_\infty$-norm) versus the number of iterations. d. Report the requested values in the Webcourses Project 4 Assignment Quiz. 6. Incorporate SOR into your Gauss-Seidel routine and repeat with relaxation parameters $\omega = 1.1, 1.2, 1.3, 1.4, 1.5$ and 1.6 and plot the residual norm versus iteration for the values of the relaxation parameter on the same plot. 7. Plot the number of iterations to convergence vs $\omega$ for values of $\omega = 1.1, 1.1, \dots 1.9$. Report the values in the Webcourses Project 4 Assignment Quiz.

          4. Set up a verification example using 3x3 system of equations (you may use the system we
discussed in class or make up your own). Make sure that you code works correctly.
5. Now solve the above system of equations using Gauss-Seidel iteration, using an initial
guess $x_i = 175$ for $i = 1, 2, \dots, N$, setting the iterative convergence criterion and the residual
norm criterion to $\epsilon = 10^{-4}$ and $\delta = 10^{-4}$. Find the:
a. the solution vector.
b. the number of iterations to convergence.
c. a plot the residual norm (use the $L_\infty$-norm) versus the number of iterations.
d. Report the requested values in the Webcourses Project 4 Assignment Quiz.
6. Incorporate SOR into your Gauss-Seidel routine and repeat with relaxation parameters
$\omega = 1.1, 1.2, 1.3, 1.4, 1.5$ and 1.6 and plot the residual norm versus iteration for the
values of the relaxation parameter on the same plot.
7. Plot the number of iterations to convergence vs $\omega$ for values of $\omega = 1.1, 1.1, \dots 1.9$. Report
the values in the Webcourses Project 4 Assignment Quiz.

4. Set up a verification example using 3x3 system of equations (you may use the system we
discussed in class or make up your own). Make sure that you code works correctly.
5. Now solve the above system of equations using Gauss-Seidel iteration, using an initial
guess xi = 175 for i = 1, 2, …, N, setting the iterative convergence criterion and the residual
norm criterion to ϵ = 10^-4 and δ = 10^-4. Find the:
a. the solution vector.
b. the number of iterations to convergence.
c. a plot the residual norm (use the L∞-norm) versus the number of iterations.
d. Report the requested values in the Webcourses Project 4 Assignment Quiz.
6. Incorporate SOR into your Gauss-Seidel routine and repeat with relaxation parameters
ω = 1.1, 1.2, 1.3, 1.4, 1.5 and 1.6 and plot the residual norm versus iteration for the
values of the relaxation parameter on the same plot.
7. Plot the number of iterations to convergence vs ω for values of ω = 1.1, 1.1, … 1.9. Report
the values in the Webcourses Project 4 Assignment Quiz.

Added by James S.

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