Math 270b: Computational Linear Algebra

Links

  • MS 7608, Mon 1-2:50pm (2 lectures) and Wed 1-1:50pm (1 lecture)

  • Prerequisits: Math 115A, 151A, and 151B, PIC 10A, basic Matlab programming

  • Online forum for Q&As, homework discussions, and projects (Sign up)

Textbooks

  1. Numerical Linear Algebra, Trefethen and Bau

  2. (supplement) Matrix Analysis for Scientists and Engineers, Laub

Workload

  • 50% five homework sets, latex required (a template is provided), 330 points in total

  • 40% final take-home exam, 264 points

  • 10% classroom and piazza participation (ask and answer questions, share resources), 66 points

  • total: 100% and 660 points

Homework / exam policy

No extension will be granted. Late submission will not be accepted. No exceptions!

Topics (tentative):

  • Othogonality, SVD, QR, (Modified) Gram-Schmidt, Householder reflectors, Givens Rotations, least squares.

  • Floating point arithmetic, conditioning, stability

  • Gaussian elimination, LU factorization, Cholesky / LDL factorization

  • Eigenvalue computation, Hessenberg, tridiagonal reduction, QR computation

  • Other topics depending on time

Homework

Policy

  • This homework assignment is open to all textbooks (listed above or not) and class notes. All solution manuals and the solutions from the previous quarters are prohibited.

  • You are encouraged to ask questions and discuss the questions and solutions on Piazza. However, copying others’ solutions or programs is considered a serious violation.

  • Please use the Latex template below.

Assignment # 1 (60 points)

  • Deadline: Saturday, Jan 16, 2015 (5 days after we finish the SVD decomposition), 11:55pm.

  • Six problems (10 points each): Trefethen-Bau 1.3, 2.5, 2.6, 3.2, 4.4, and 5.4. (Half of the problems are not covered in lectures. They are extensions to the lectures.)

  • Template: latex / pdf. Compile it to a PDF file before submission.

  • Submit your homework on UCLA CCLE. Submission will be closed after the deadline.

Assignment # 2 (70 points)

  • Deadline: Saturday, Jan 30, 11:55pm.

  • Seven problems (10 points each): Trefethen-Bau 6.3, 6.4, 7.1, 7.5, 8.3, 10.4, 11.3 (Some problems are not covered in lectures. They are extensions to the lectures.)

  • Use the template of HW1 above. Please change “HW1” to “HW2” and add the seventh problem. As usual, compile into one PDF file before submission.

  • Submit your homework on UCLA CCLE. Submission will be closed after the deadline.

Assignment # 3 (70 points)

  • Deadline: Saturday, Feb 13, 11:55pm.

  • Four problems: Trefethen-Bau 12.1 (10 pts), 13.4 (20 pts, use the Matlab symbolic toolbox), 15.1 (20 pts), 15.2 (20 pts)

  • Use the template of HW1 above. Please change “HW1” to “HW3”. As usual, compile into one PDF file before submission.

  • Submit your homework on UCLA CCLE. Submission will be closed after the deadline.

Assignment # 4 (70 points)

  • Deadline: Saturday, Feb 27, 11:55pm.

  • Six problems: Trefethen-Bau 17.2 (10 pts), 19.2 (10 pts), 20.2 (10 pts), 20.4 (10 pts) 21.6 (10 pts), 24.1 (20 pts)

  • Use the template of HW1 above. Please change “HW1” to “HW4”. As usual, compile into one PDF file before submission.

  • Submit your homework on UCLA CCLE. Submission will be closed after the deadline.

Assignment # 5 (60 points)

  • Deadline: Saturday, Mar 12, 11:55pm.

  • Six problems: Trefethen-Bau 25.3 (15 pts, 5 pts for each case), 26.1 (20 pts), 28.3 (10 pts), 30.3 (15 pts)

  • Use the template of HW1 above. Please change “HW1” to “HW5”. As usual, compile into one PDF file before submission.

  • Submit your homework on UCLA CCLE. Submission will be closed after the deadline.


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