Final version.

1.  During the quiz you may use your textbook, my notes, 
scribed notes, and your own notes.

2.  No calculators or other electronic devices are permitted.

3.  Please make sure your cell phones are quiet during class and
off during quizzes.


For Quiz 6, be able to:


-- Explain why the Krylov methods terminate in at most
   n iterations with the exact solution.

-- Count the work per iteration for the Arnoldi algorithm
   or the cg algorithm.

-- Determine the storage requirements for the Arnoldi
   algorithm or the cg algorithm.

-- Given definition of "Z", determine how to solve the
   linear system of equations in order to determine
   the vector "y" for one of the Krylov subspace methods.
   (Example: top of p.9 of notes)

-- Use the convergence results for GMRES.

     Example:  Show that if G-hat has only 5 distinct 
     eigenvalues, then GMRES must terminate in at most 
     5 iterations with the true solution.

     Example: Show that if G-hat has 5 small clusters of
     eigenvalues, then after 5 iterations, GMRES produces
     a good approximate solution.

-- Use the convergence results for CG.

-- Implement a preconditioning algorithm such as
   Gauss-Seidel or SOR.

-- Transfer values between grids in multigrid, given 
   a restriction operator and an interpolation operator.

-- Form a sequence of nested grids.

-- Explain or use the V-cycle and nested grids algorithms.