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 5, be able to:

-- Use monotonicity to compute upper and lower bounds
   on eigenvalues, given eigenvalues for inscribed and
   circumscribed regions.

-- Apply the theorems on accuracy of computed eigenvalues
   and eigenfunctions.

-- Convert a matrix from its (usual) dense representation
   to sparse format, and from sparse format to dense.

-- Determine what elements of a matrix fill in when doing
   Cholesky factorization.

-- Determine which elements are in the profile of a matrix.

-- Given a sparse matrix, determine its graph.  Given
   a graph, determine the sparsity of the corresponding matrix.

-- Apply our reordering strategies (Cuthill-McKee, minimum
   degree, and nested dissection) to a given graph.

-- Apply J, GS, or SOR to a given system of linear equations
   (algebraically or geometrically).

-- Construct a basis for a Krylov subspace and, in particular,
   contruct an orthogonal basis.

-- 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)