Use GMRES to solve the system in Exercise 9.4.33. Compare the rate of convergence with the CG algorithm in Exercise 9.6.8.

Data From Exercise 9.4.33

The matrix arises in the finite  difference (and finite element) discretization of the Poisson equation on a nine point square  grid. Solve the linear system Au = e₅ using 

Data From Exercise 9.6.8

Use the Conjugate Gradient Method to solve the system in Exercise 9.4.33. How many  iterations do you need to obtain the solution that is accurate to 2 decimal places? How  does this compare to the Jacobi and SOR Methods?

Data From Exercise 9.4.33

The matrix arises in the finite  difference (and finite element) discretization of the Poisson equation on a nine point square  grid. Solve the linear system Au = e₅ using

Transcribed Image Text:

0 -1 A= 0 0 0 0 0 -1 4 -1 . 0 0 0 0 0 -1 4 0 0 0 0 0 0 0 4 -1 0 -1 0 0 0 0 ܘܟܘ -1 -1 4 0 -1 -1 0 0 0 . . 0 . 0 -1 0 -1 0 4 -1 -1 4 -1 a••C••7 -1 0 0 -1 0 4 0 0 0 -1 0 0 0 0 0 -1 4