Sept 6, 1995, 11:10am

There was a small typo in Question 1.9. It has been repaired in the on-line version of chapter 1.

Sept 13, 1995, 2:24pm

The second homework assignment is to do problems 2.1, 2.3, 2.4, 2.5, 2.8, and either 2.9 or 2.10. The others are fair game for extra credit. These numbers refer to the on-line version of chapter 2, not the version you bought from the math department. It will be due in 2 weeks, though I might add a little time for the programming question, question 2.5.

Sept 25, 1995, 10:03pm EST

The 2nd homework is due Friday, Sept 29.

Sept 28, 1995, 11:20am

There are some bugs in the homework: 1) The problem says to compute the "ratio of eps/RCOND to the true error," and that this should be O(1) or O(n), i.e. the error bound should not overestimate the true error by much. But occasionally, if you are lucky, the true error will in fact be zero, in which case this ratio will be infinite. So instead, print the "ratio of the true error to eps/RCOND", which ideally should be less than or equal to one, and usually not too small (unless you are "lucky" and it is zero). 2) The "scaled backward error R" and "backward error BERR" should be close to machine epsilon, not 1. So print the ratios R/eps and BERR/eps instead. Also, we will meed in 306 Soda on Friday, 9/28, not in 405 Soda.

Oct 2, 1995, 7:45am

Please do all the problems at the end of chapter 3 (the on-line version). They are due Friday Oct 13.

Oct 11, 1995, 2:40pm

There is a typo in problem 3.6. The matrix [A;B] should be [A;C].

Oct 26, 1995, 9:00am

The homework at the end of Chapter 4 is due Friday, Nov 3.

Nov 12, 1995, 11:00pm

The homework at the end of Chapter 5 is due Monday, Nov 20. Do all the problems without stars, and one of the starred problems. You can do other starred problems for extra credit.

Nov 20, 1995, 10:30pm

The homework for Chapter 5 is now due Wednesday, Nov 22, instead of Monday.

Nov 20, 1995, 10:45pm

In question 5.9, you should assume Rayleigh Quotient Iteration starts with x_0 = [0, ... , 0, 1]^T.

Nov 20, 1995, 11:12pm

In question 5.11, the fraction 5/4 should be 4/3.

Nov 21, 1995, 10:00am

Here are some hints for the last question, 5.13. Flipping X means
replacing X by JXJ, where J is the identity matrix with its
rows in reverse order. If L is any lower triangular matrix,
then JLJ is upper triangular. Some intermediate facts that you
might want to prove are that (in Latex notation)

\hat{A}_{s+1} = (L_1 ... L_s)^T \hat{A}_1 (L_1 ... L_s)^{-T}

Let the sequence of QR iterates be defined by A_s = Q_s R_s and
A_{s+1} = R_s Q_s. Then the QR decomposition of A_1^s is

A_1^s = (Q_1 ... Q_s) ( R_s ... R_1 )


Nov 27, 1995, 7:48am

The last homework set consists of the unstarred problems in Chapter 7.
It is due Monday, Dec 11.

Nov 29, 1995, 6:00pm

There is a typo in Lemma 7.7, which you are to prove:
The third property should be:
T_m(x) = 2^(m-1) x^m + O(x^(m-1))

Nov 29, 1995, 7:20pm

There are two more typos in Lemma 7.7, which you are to prove:
First, the first property in Lemma 7.7 is the definition of
Chebyshev polynomials, so there is nothing to prove. Second,
the last property in Lemma 7.7 should be:
T_m(1+2*epsilon) \approx 1 + 2*m*sqrt(epsilon)

Dec 4, 1995, 11:07am

In the description of Domain Decomposition in the notes,
A_{23}^T A_{11}^{-1} should be A_{23}^T A_{22}^{-1} in
both places where it appears (on page 198 of the hard-copy
notes, or page 272 of the on-line notes).

Dec 8, 1995, 1:40pm

The final will be "open everything."

Dec 8, 1995, 4:30pm