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

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: Wednesdays, 1:00pm-1:50pm.
Grader Minxin Zhang
Email: miz151 AT ucsd DOT edu
Office Hours: Thursdays 3:30-5:30 in AP&M 6446
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 Homework will announced on every other Friday after lecture. Homework can be submitted to the mailboxes on every other Fridays before 2pm in the afternoon (before the lecture starts). All submissions must be in handed-in in handwritten form.
Grading The final grade will composed by 50% of the homework and by 50% of the final exam.
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.
Textbook resources The following textbooks are recommended to supplement the lectures: Your experience in numerical linear algebra will greatly benefit from a solid background in linear algebra. Your instructor recommends the following textbooks as helpful references: Even though sparse direct methods will not be in the focus of this course, your instructor recommends the following two references to the interest student:
Additional Resources A collection of notes and articles that supplement the course content:
  • Notes on the Singular Value Decomposition. [Link]
  • E. Wallace Floating-Point Toy. [Link]
  • Lloyd N. Trefethen, The Definition of Numerical Analysis. [Link]
  • 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

Homework

  1. Homework 1 - Solutions 1
  2. Homework 2 - Solutions 2
  3. Optional Programming Homework 1 - Python script
  4. Homework 3
  5. Optional Programming Homework 2
  6. Homework 4

Course Calendar

Lecture Content
# 1, 0F
28.09.2018.
Administrative. Outline of Numerical Linear Algebra. I.1: Simple algorithms. Homework 1 announced. Intro Slides
# 2, 1M
01.10.2018.
I.2: Solving triangular systems of equations.
# 3, 1W
03.10.2018.
I.3: Inverting triangular matrices. I.4: LU decomposition.
# 4, 1F
05.10.2018.
I.4: LU decomposition, continued.
# 5, 2M
08.10.2018.
I.5: LU decomposition with pivoting.
# 6, 2W
10.10.2018.
I.5: LU decomposition with pivoting, Diagonally dominant matrices.
# 7, 2F
12.10.2018.
I.6: LDLT decomposition. SPD matrices. Homework 1 collected. Homework 2 announced.
# 8, 3M
15.10.2018.
I.7: Cholesky factorization. II.1: QR decomposition.
# 9, 3W
17.10.2018.
II.2: Gram-Schmidt orthogonalization.
# 10, 3F
19.10.2018.
II.3: QR decomposition using Givens rotations.
#11, 4M
22.10.2018.
II.3: QR decomposition using Givens rotations. II.4: QR decomposition using Householder reflections.
#12, 4W
24.10.2018.
II.5: Least-Squares Problems of Full Rank.
#13, 4F
26.10.2018.
II.5: Least-Squares Problems of Full Rank. 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.
III.1 Least-Squares Problems and their solvability. III.2 Least-Squares Problems and the Pseudoinverse.
#15, 5W
31.10.2018.
III.3 Schur decomposition and Singular Value Decomposition.
#16, 5F
02.11.2018.
III.3 Singular Value Decomposition and Pseudoinverse
#17, 6M
05.11.2018.
III.3 Direct Methods recapitulated. Direct Method Slides IV.1: Banach fixpoint theorem
#18, 6W
07.11.2018.
IV.2: Classical iterative methods via fixpoint theory, Spectral radius, and Convergence theory.
#19, 6F
09.11.2018.
IV.3: Gerschgorin circle theorem. Convergence of classical Richardson iteration. Homework 3 collected. Homework 4 announced.
#20, 7M
12.11.2018.
Veteran's Day Holiday
#21, 7W
14.11.2018.
IV.4: Jacobi method and Gauss-Seidel method.
#22, 7F
16.11.2018.
IV.5: Over-relaxation methods.
#23, 8M
19.11.2018.
V.1: Gradient descent and its convergence.
#24, 8W
21.11.2018.
V.1: Gradient descent and its convergence.
#25, 8F
23.11.2018.
Thanksgiving Holiday
#26, 9M
26.11.2018.
V.2: Method of Conjugate Gradients. Homework 4 collected. Homework 5 announced.
#27, 9W
28.11.2018.
V.2: Method of Conjugate Gradients.
#28, 9F
30.11.2018.
VI.1 Eigenvalue Problems via Power Iteration
30.11.2018: Deadline to with "W" grade on transcript.
#29,10M
03.12.2018.
VI.1 Eigenvalue Problems via Inverse Iteration
#30,10W
05.12.2018.
VI.1 Eigenvalue Problems via QR algorithm.
#31,10F
07.12.2018.
Recapitulation of material.
FI
12.12.2018.
Final Exam. TBA 3:00pm - 5:59pm. Place to be announced.