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GMRES Stagnation

  1. Apr 1, 2009 #1
    1. The problem statement, all variables and given/known data
    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 = e1 and x0-0. Show that ||rk||2=||r0||2 for k=1,2,3.

    Here, rk=Axk-b where xk is the iterate produced by GMRES in iteration k.

    Finding r0 is not a problem for me since x0 is the zero vector. Therefore, ||r0||= 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 x1,x2, and x3 explicitly, but I have no idea how to show that ||rk||2=b for k=1,2,3. Can anyone push me in the right direction? Thank you.
     
  2. jcsd
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