Math 270b: Computational Linear Algebra

Links

  • MS 5148, Mon Wed Fri 11-11:50am

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

  • Online forum for Q&As, homework discussions, and projects

Textbooks

  1. Numerical Linear Algebra, Trefethen and Bau

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

Workload

  • 50% homework sets, latex required (a template is provided), 500 points in total

  • 40% projects, 400 points

  • 10% classroom and piazza participation (ask and answer questions, share resources), 100 points

  • total: 100% and 1000 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: Friday, Jan 26, 2018, 11:59pm

  • Six problems (10 points each): Trefethen-Bau 1.3, 2.5, 2.6, 3.2, 4.4, and 5.4. (Some 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 (60 points)

  • Deadline: Wednesday, Feb 7, 11:59pm.

  • Six problems (10 points each): Trefethen-Bau 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.” 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 24, 11:59pm.

  • Seven problems: Trefethen-Bau 12.1 (10 pts), 15.1 (10 pts), 15.2 (20 pts), 19.2 (10 pts), 20.2 (10 pts), 20.4 (10 pts), 21.6 (10 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, Mar 17, 11:59pm.

  • Six problems: Trefethen-Bau 24.1 (10 pts), 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 “HW4”. 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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