Question: 03-22-2010: What is the due date? How should I submit it?
Answer: This assignment is due at 4:00pm on Monday, April 5. Late penalties begin at 4:01 on Tuesday, April 6 . There are two acceptable ways to submit it: (1) Give it to me in the classroom, before class begins. (2) Deliver it to my office, any time prior to when I leave for class on the due date. (Slide it under the door if I am not there.) Do not put it in my mailbox, and do not leave it in my office after I leave for class on the due date. Email submission is acceptable only in "emergencies".
Question: 03-22-2010: What are the point values for the challenges?
Answer:
30 points total.
Program documentation and labeling of plots: 4 points.
Challenge 1a: 4 points.
Challenge 1b: 12 points.
Challenge 1c: 6 points for discussion.
Challenge 2 : 4 points.
Question: 03-22-2010: What should I submit?
Answer: I grade everyone's Challenge 1, then everyone's 2, etc., to help insure uniformity in grading, so I would really appreciate your help in making this easy.
Grading notes:Question: 03-24-10: In challenge 1, should we solve the linear systems using "backslash" on the reordered matrices?
Answer: You need to do the Cholesky decomposition, because I ask for the number of nonzeros, so solve using the factor L by "x = (L') \ (L \ b)".
Question: 03-24-10: How should we measure the error?
Answer: Use the 2-norm: ||z|| = sqrt(z'*z). In Matlab this is just "norm(z)".
Question: 03-25-10: I'm having trouble getting pcg to converge in Challenge 1.
Answer:
Yes, that is a particularly difficult b vector for this matrix.
You might contrast the behavior for this right-hand side vector b:
n = 10848;
xt = ones(n,1);
b = Problem.A * xt;
Maybe working with this b will be more revealing.
04-02-2010 In particular, "[x,fl,relres] = pcg(Problem.A,b);" should terminate in 20 iterations with relres= 1.5443e-04.
Question: 03-28-2010 In Challenge 2, you want us to find the "smallest" eigenvalues; I take this to mean the smallest in absolute value. Is that correct?
Answer: No, I mean the leftmost ones when they are plotted.
Question: 03-30-2010 In Challenge 2 of the homework, can we use the 'sa' command with eigs to find the 6 smallest eigenvalues? Or is using a sigma mandatory?
Answer: You may use 'sa' if you include in your documentation a few sentences on how it works. Use 'type eigs' to look at the Matlab program.
Question: 04-03-10 I can not understand what the options of preconditioning are. Are they the droptol, rdiag? And these command produce an upper triangula matrix.
Answer: In our usual notation, the Cholesky factorization is L L'. In cholinc, the factorization is R' R. So R = L'.
The options are droptol (set all elements with abs val less than droptol to zero), rdiag (don't allow zeros on the main diag of R), and michol (use a slight variant of the algorithm).
Question: 04-03-10 So how do we use pcg? Do we need to change the vector?
Answer: Use R' and R as the 5th and 6th arguments to pcg. Don't change b unless you reordered.
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Answer: