Math 270A -- Numerical Linear Algebra -- Fall 2018

Under Construction.

Lecture site: AP&M 2402
Lecture times: Monday, Wednesday, Friday. 2:00pm-2:50pm.
Final Exam
time and place
December 12th, 2018, 3:00pm - 5:59pm. Place to be announced.
Instructor Martin Licht
Email: mlicht AT ucsd DOT edu
Office: AP&M 5880E
Hours: TBA. 10-11pm.
Grader TBA
Email: TBA AT ucsd DOT edu
Office Hours: TBA ?-?pm in AP&M TBA
Section 949162
Credit Hours: 4 units
Course content Error analysis of the numerical solution of linear equations and least squares problems for the full rank and rank deficient cases. Error analysis of numerical methods for eigenvalue problems and singular value problems. Iterative methods for large sparse systems of linear equations. Prerequisites: graduate standing or consent of instructor.
Formal prerequesite Graduate standing or consent of instructor.
Homework information Homework will announced on WEEKDAYs after lecture. Homework can be submitted to the mailboxes on WEEKDAYs before 11am in the morning (before the lecture starts), or that the very beginning of WEEKDAY's lecture. All submissions must be in handed-in in handwritten form.
Academic Integrity Every student is expected to conduct themselves with academic integrity. Violations of academic integrity will be treated seriously. See http://www-senate.ucsd.edu/manual/Appendices/app2.htm for UCSD Policy on Integrity of Scholarship.

Announcements

Grading Information

The final grade will composed 20% homework and either (a) 20% of the first midterm, and 20% of the second midterm, and 40% of the final exam or (b) 20% of the best midterm and 60% of the final exam, depending on what gives the better result.

Your course grade will be determined by your cumulative average at the end of the quarter, based on the following scale:

A+ A A- B+ B B- C+ C C-
100 - 96.66 96.65 - 93.33 93.32 - 90.00 89.99 - 86.66 86.65 - 83.33 83.32 - 80.00 79.99 - 76.66 76.65 - 73.33 73.32 - 70

The above scale is guaranteed: for example, if your cumulative average is at least 73, then your final grade will be at least B. However, your instructor may adjust the above scale to be more generous.

Homework

  1. Week One Exercises - Week One Exercise Solutions
  2. Homework 1 - Solutions 1
  3. Homework 2 - Solutions 2
  4. Practice for the First Midterm - Solution for First Midterm
  5. Homework 3 - Solutions 3
  6. Homework 4 - Solutions 4
  7. Homework 5 - Solutions 5
  8. Homework 6 - Solutions 6
  9. Practice for the Second Midterm
  10. Homework 7
  11. Homework 8 Solutions 8
  12. Practice for Final

Course Calendar

Lecture Content
# 1, 0F
28.09.2018.
Administrative. Outline of Numerical Linear Algebra. Simple algorithms. Homework 1 announced.
# 2, 1M
01.10.2018.
Simple algorithms. Inverting simple systems.
# 3, 1W
03.10.2018.
LU decomposition. Pivoting.
# 4, 1F
05.10.2018.
Cholesky decomposition.
# 5, 2M
08.10.2018.
QR decomposition using Gram-Schmidt orthogonalization.
# 6, 2W
10.10.2018.
QR decomposition using Givens rotations and Householder reflections.
# 7, 2F
12.10.2018.
Interlude: condition numbers. Homework 1 collected. Homework 2 announced.
# 8, 3M
15.10.2018.
Classical iterative methods. Convergence theory.
# 9, 3W
17.10.2018.
Preconditioning. Convergence of Richardson iteration with scalar preconditioning.
# 10, 3F
19.10.2018.
Jacobi preconditioning.
#11, 4M
22.10.2018.
Gauss-Seidel preconditioning.
#12, 4W
24.10.2018.
Over-relaxation methods.
#13, 4F
26.10.2018.
Iterative refinement. Homework 2 collected. Homework 3 announced.
26.10.2018: Deadline to change grading option, change units, and drop classes without "W" grade on transcript.
#14, 5M
29.10.2018.
Gradient descent. Convergence.
#15, 5W
31.10.2018.
Methods of Conjugate Gradients.
#16, 5F
02.11.2018.
Methods of Conjugate Gradients.
#17, 6M
05.11.2018.
Methods of Conjugate Gradients.
#18, 6W
07.11.2018.
#19, 6F
09.11.2018.
Homework 3 collected. Homework 4 announced.
#20, 7M
12.11.2018.
Veteran's Day Holiday
#21, 7W
14.11.2018.
#22, 7F
16.11.2018.
#23, 8M
19.11.2018.
#24, 8W
21.11.2018.
#25, 8F
23.11.2018.
Thanksgiving Holiday
#26, 9M
26.11.2018.
Homework 4 collected. Homework 5 announced.
#27, 9W
28.11.2018.
#28, 9F
30.11.2018.
Homework 8 collected.
30.11.2018: Deadline to with "W" grade on transcript.
#29,10M
03.12.2018.
#30,10W
05.12.2018.
#31,10F
07.12.2018.
FI
TBA.
Final Exam. TBA 11:00pm - 2:59pm. Place to be announced.

Course Material and Additional Resources

D. Goldberg, What every computer scientist should know about Floating-Point arithmetics [Link]

J. R. Shewchuk, The conjugate gradient method without the agonizing pain [Link]

Helpful Links

Important academic dates for this academic year