Introduction to Numerical Analysis: Linear Algebra
Math 170A -- Spring 2019

Lecture site: SOLIS 104
Lecture times: Monday, Wednesday, Friday. 2:00pm-2:50pm.
Discussion sessions B01 957530: Thursday 5:00p-5:50p, AP&M 7421 with Saeed Vahidian
B01 957531: Thursday 6:00p-6:50p, AP&M 7421 with Saeed Vahidian
B01 957532: Thursday 7:00p-7:50p, AP&M 7421 with Zequn Zheng
B01 957533: Thursday 8:00p-8:50p, AP&M 7421 with Zequn Zheng
Final Exam
time and place
March 18th, 2019, 3:00pm - 5:59pm. Place to be announced by department.
Instructor Martin Licht
Email: mlicht AT ucsd DOT edu
Office: AP&M 5880E
Hours: Wednesday, 1-2pm.
Teaching Assistant Saeed Vahidian
Email: svahidia AT ucsd DOT edu
Office Hours: TBA, MHA 5722
Teaching Assistant Zequn Zheng
Email: zez084 AT ucsd DOT edu
Office Hours: Th 2pm-6pm, AP&M 6436
Section(s) 957530, 957531, 957532, 957533
Credit Hours: 4 units
Course content Analysis of numerical methods for linear algebraic systems and least squares problems. Orthogonalization methods. Ill conditioned problems. Eigenvalue and singular value computations. Knowledge of programming recommended.
Formal prerequesite Math 18 or Math 20F or Math 31AH, and Math 20C. Students who have not completed the listed prerequisites may enroll with consent of instructor.
Homework information Homework will announced on Fridays after lecture. Homework can be submitted to the mailboxes (AP&M basement) on Fridays before 3:30pm. 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.
Resources The textbook for this lecture is:
  • Watkins, Fundamentals of Matrix Computations.
The following textbooks are recommended to supplement the lectures: Some information about floating point arithmetics:
  • D. Goldberg, What every computer scientist should know about Floating-Point arithmetics. [Link]
  • Information about Floating-Point numbers. [Link]
  • E. Wallace Floating-Point Toy. [Link]
Your experience in numerical linear algebra will greatly benefit from a solid background in linear algebra. Your instructor recommends the following textbook as a helpful reference: Assorted links to additional material:
  • Lloyd N. Trefethen, The Definition of Numerical Analysis. [Link]
  • J. R. Shewchuk, The Conjugate Gradient Method without the Agonizing Pain. [Link]
Helpful links

Grading Information

The final grade will be composed as follows: 20% homework, 20% midterm, and 60% final exam.

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.

Course Calendar

Lecture Content
# 1, 1M
07.01.2019.
Administrativa. Examples and Motivation.
Part 1: Floating-Point Numbers
# 2, 1W
09.01.2019.
Part 1: Floating-Point Numbers
# 3, 1F
11.01.2019.
Part 1: Floating-Point Numbers
# 4, 2M
14.01.2019.
Part 2: Linear Algebra on a computer
# 5, 2W
16.01.2019.
Part 2: Linear Algebra on a computer
# 6, 2F
18.01.2019.
Part 2: Linear Algebra on a computer
Homework 1 & 2 announced.
# 7, 3M
21.01.2019.
Martin Luther King, Jr. Holiday
# 8, 3W
23.01.2019.
Part 3: Invertibility
# 9, 3F
25.01.2019.
Part 3: Invertibility
#10, 4M
28.01.2019.
Part 4: LU decomposition and Cholesky factorization
#11, 4W
30.01.2019.
Part 4: LU decomposition and Cholesky factorization
#12, 4F
01.02.2019.
Part 4: LU decomposition and Cholesky factorization
Homework 3 collected. Homework 1 & 2 collected. Homework 3 & 4 announced.
01.02.2019: Deadline to change grading option, change units, and drop classes without "W" grade on transcript.
#13, 5M
04.02.2019.
Part 5: Sensitivity of Linear Systems
#14, 5W
06.02.2019.
Part 5: Sensitivity of Linear Systems
#15, 5F
08.02.2019.
Part 5: Sensitivity of Linear Systems
#16, 6M
11.02.2019.
Midterm.
#17, 6W
13.02.2019.
Part 6: Gram-Schmidt process and QR factorization
#18, 6F
15.02.2019.
Part 6: Gram-Schmidt process and QR factorization
Homework 3 & 4 collected. Homework 5 & 6 announced.
15.02.2019: Deadline to drop with "W" grade on transcript.
#19, 7M
18.02.2019.
Presidents' Day Holiday
#20, 7W
20.02.2019.
Part 6: Gram-Schmidt process and QR factorization
#21, 7F
22.02.2019.
Part 6: Gram-Schmidt process and QR factorization
#22, 8M
25.02.2019.
Part 6: Gram-Schmidt process and QR factorization
#23, 8W
27.02.2019.
Part 7: Iterative Methods
#24, 8F
01.03.2019.
Part 7: Iterative Methods
Homework 5 & 6 collected. Homework 7 & 8 announced.
#25, 9M
04.03.2019.
Part 7: Iterative Methods
#26, 9W
06.03.2019.
Part 7: Iterative Methods
#27, 9F
089.03.2019.
Part 7: Iterative Methods
Homework 7 & 8 collected. Practice Material for Final available..
#28,10M
11.03.2019.
Part 8: Eigenvalue Calculation
#29,10W
13.03.2019.
Part 8: Eigenvalue Calculation
#30,10F
15.03.2019.
Part 8: Eigenvalue Calculation
FI
18.03.2019.
Final Exam. 3:00pm - 5:59pm. Place to be announced.