Math 128A, Fall
2009
I teach two discussion sections for Prof John Strain's Math 128A class.
Section 101 meets Wednesday 9am-10am in B3A Evans (in the basement)
Section 102 meets Wednesday 10am-11am in B3A Evans (in the basement)
My office - 787 Evans
My office hours:
Monday
9.30-10.30am
Wednesday
1-3pm
Friday
1-2pm
My e-mail:
Announcements
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Problem Set 11 is posted, due Wednesday November 25 by 5 pm. Solve problems 2, 3, 5, 6 and 7 from Section 9.11 of Quarteroni, Sacco and Saleri.
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Problem Set 12 is posted, due Friday December 4 by 5 pm. Solve problems 1, 5, 8 and 9 from Section 10.14 of Quarteroni, Sacco and Saleri.
Course Web
Page
contains important information, including course policies.
Textbook
Required Text:
A Quarteroni, R Sacco and F Saleri, Numerical Mathematics.
Supplementary texts:
Otto and Denier, An Introduction to Programming and Numerical Methods in MATLAB
and
Quarteroni and Saleri, Scientific Computing with MATLAB and Octave.
The links lead to the online version of the books on publisher's website. It can be accessed on any computer connected to UC Berkeley network. If you need to access those links from off-campus, you can setup a proxy through the library. Click here for instructions.
Software
In order to complete the programming exercises you can use one of the two following programs:
- Matlab
- GNU Octave. GNU Octave is a free and open-source program, whose syntax is almost identical to Matlab's. Octave can be downloaded for the following operating systems:
- Linux binaries or from your distribution package manager.
- Mac OS X Intel and PowerPC versions.
- Windows installer.
- Windows (option two) is to install Cygwin Linux emulator and select Octave and GNUPlot packages. You will also need to install X-Windows emulator("xinit" package).
You can come to Evans basement lab to work with Matlab. Check the schedule of drop-in hours.
Matlab programming class
The Math 98 class (Introduction to MATLAB programming) is highly recommended, it is nevertheless neither necessary nor required. You can still ask me Matlab and Octave questions, regardless whether you take Math 98 or not.
Homework
The homework is to be submitted by 5pm Wednesday of the week it is due and to be returned in the discussion of the following Wednesday. In particular, late homework will not be accepted.
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Problem Set 1 (due Wednesday September 2 by 5 pm): Solve problems 2, 5, 7, 12 and 13 from Section 1.13 of Quarteroni, Sacco and Saleri.
Note: In problem 12, A^T should be A^H since A is complex. In problem 13, the statement should read "is the unique minimum Frobenius norm solution to" the displayed minimization problem.
- Problem Set 2 (due Wednesday September 9 by 5 pm):
Solve problems 14, 15, 16 and 17 from Section 1.13 and problems 1, 2 and 5 from Section 2.6 of Quarteroni, Sacco and Saleri.
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Problem Set 3 (due Friday September 18 by 5 pm): Solve problems 9, 10, 11, 12 and 13 from Section 2.6 of Quarteroni, Sacco and Saleri.
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Problem Set 4 (due Friday September 25 by 2 pm): Solve problems 1,2,3,4,9 and 10 from Section 3.15 of Quarteroni, Sacco and Saleri.
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Problem Set 5 (due Friday October 2 by 2 pm): Solve problems 12, 13, 14, and 15 from Section 3.15 of Quarteroni, Sacco and Saleri.
Problem 5: write, debug and test Matlab (or other convenient language) programs
for (a) applying the Householder reflection H(u) = I-2 u u^T for given unit vector u to a vector x,
(b) computing the unit vector u which stably transforms a given vector x to zero below given entry j,
and (c) computing the QR factorization of an invertible square matrix A.
(d) Test the QR factorization on Hilbert matrices A(i,j)=1/(i+j-1) of orders n= 1:20,
and tabulate the Frobenius norms of Q^T Q - I, Q Q^T - I, and A - QR.
(e) Compare these residuals with the condition number of A (which is O(e^(7n/2)).
(f) Sharpen your results (where possible) by iterative improvement:
compute fl( Q^T A) explicitly in finite precision arithmetic (even though it should be upper triangular in exact arithmetic),
refactorize as fl(Q^T A) = Q_1 R_1, and replace Q by Q Q_1.
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Problem Set 6 (due Friday October 9 by 2 pm): Solve problems 2,3,5,8 and 10 from Section 6.15 of Quarteroni, Sacco and Saleri.
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Problem set 7 (due Friday October 16 by 2pm) is here
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Problem set 8 (due Friday October 30 by 2 pm): Solve problems 6 and 7 from Section 7.5 of Quarteroni, Sacco and Saleri.
Use Program 50 for Newton's method, and repeat problem 7 with Broyden's method (Program 58) and discuss the results.
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Problem Set 9 (due Friday November 6 by 2 pm): Solve problems
1, 2, 4 and 5 from Section 8.9 of Quarteroni, Sacco and Saleri.
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Homework 10 (due Friday November 13 by 2 pm). Solve problems 7, 12 and 13 from Section 8.9 of Quarteroni, Sacco and Saleri.
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Problem Set 11 (due Wednesday November 25 by 5 pm): Solve problems 2, 3, 5, 6 and 7 from Section 9.11 of Quarteroni, Sacco and Saleri.
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Problem Set 12 (due Friday December 4 by 5 pm): Solve problems 1, 5, 8 and 9 from Section 10.14 of Quarteroni, Sacco and Saleri.
Note:A^B is to be understood as "Power B of A". A^T means "Transpose of A".
Handouts and code
Past Exams and Midterms
Math Department Math128A Exam and Midterm archive
Useful Links