Let A be the 4x4 matrix with elements in positions (1,2), (2,3), (3,4), and (4,1) equal to 1, and all other elements equal to zero. Let b = =0. Show that for k=1,2,3.
Here, where is the iterate produced by GMRES in iteration k.
Finding is not a problem for me since is the zero vector. Therefore, = b. However, we have not learned how to actually figure out the different iterations, so I'm guessing that we do not have to find , , and , explicitly, but I have no idea how to show that =b for k=1,2,3. Can anyone push me in the right direction? Thank you.