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Instructor Spring 2023

Rebecca Morrison

Office: ECOT 820��

Email: rebeccam@colorado.edu

Class details��

Class meetings: T/Th 9:30 – 10:45 , ECCR 105��

Grader: Viveka Salinamakki, viveka.salinamakki@colorado.edu��

Office hours: RM : Mon 10:30 – 11:30a, ECOT 820, and by appointment

Materials

Numerical Linear Algebra by Trefethen and Bau��

Lecture notes (R.Morrison)��

Canvas for announcements, class recordings, and grading��

Slack for questions about the course and student - led discussions (See Canvas for link)��

Note about email: Email should be used only for personal/individual matters, and even then it is better to come see me in person. Any emails about the class content, logistics, etc. will be posted on Slack and answered for everyone there.

Course Description

This course will cover the fundamental ideas of numerical linear algebra, which, as Trefethen and ��Bau point out in their preface, is “really applied linear algebra.” They go further: “Numerical linear algebra is really functional analysis, but with the emphasis always on practical algorithmic ideas rather than mathematical technicalities.” In this class, we will develop some of the theory and get lots of practice with examples. Topics include the basics (matrix operations, norms, and the SVD), QR factorization and least squares, conditioning and stability, systems of equations, eigen values, and, time permitting, iterative methods.

Course Objectives

In this course, students will learn how to:

• Perform common matrix operations, compute and manipulate norms, and become comfortable with complex matrices and vectors
• Compute the Singular Value Decomposition (SVD) by hand for small matrices and implement it on a computer
• Leverage the QR factorization for many other purposes
• Compute and compare conditioning and stability of various modern and historical algorithms
• Solve systems of equations
• Find eigenvalues
• Begin to analyze common iterative methods
• Appreciate numerical linear algebra for the "beautiful and fundamental" subject that it is!

Course outline

W1 (8/29,8/31) Introductions ,Syllabus, L1: Matrix - vector multiplication��

W2 (9/5,9/7) L2: Orthogonal vectors & matrices��

W3 (9/12,9/14) L3: Norms��

W4 (9/19,9/21) L4-5: SVD��

W5 (9/26,9/28) L6: Projectors ; L7-8: QR & Gram-Schmidt��

W6 (10/3,10/5) L10: House holder, L11: Least squares��

W7 (10/10,10/12) L12: Condition numbers��

W8 (10/17,10/19) L13: Floating point, L14-15: Stability, (L16-19: S&C of some algorithms)��

W9 (10/24,10/26) L20: Gaussian Elimination, L21: Pivoting��

W10 (10/31,11/2) L22: Stability of GE, L23: Cholesky��

W11 (11/7,11/9) L24-25: Eigen value problems & algorithms, L26-27: Reductions, Rayleigh quotient��

W12 (11/14,11/16) L28-29: QR with & without shifts, L30-31: Other algorithms, SVD��

W13 (11/21,11/23) Fallbreak��

W14 (11/28,11/30) Flex week��

W15 (12/5,12/7) L32-34: Overview of iterative methods, Arnoldi; L36-37: Lanczos, Gauss quadrature��

W16 (12/12,12/14) L38: Conjugate gradients, L40: Preconditioning��

Note: that this schedule is approximate and subject to modifications.

Course work and grading

Grades will be determined based on homeworks.

• Homework: Homeworks will be assigned approximately every two weeks. You will be asked to upload a pdf (of hand written exercises, typed exercises, and/or a Jupyter notebook or other code). You may complete homework assignments in groups, but please turn in your own work, and make sure you understand each step. If you are very sure that the homework has been misgraded, you may contact Viveka directly (and cc me). Otherwise, please accept the grade and try to understand what you could do better or make clearer next time.

– Home work drop: The last homework is optional and, if completed, its score will replace the lowest homework grade.��

– Late policy: Because of the large classsize, late homework will not be accepted (in general).

• Extra credit: Turn in a nice, clean, edited draft of class notes, in LaTeX. This must be emailed to me by the start of the following Tuesday class period. We will have a sign-up sheet if needed (i.e., if I start receiving lots of duplicates). Every (acceptable) day of notes will add 1% to your final grade.

• More extra credit: If you would like your typed, LaTeX’d homework solutions to be considered for extra credit, please flag Viveka. If you get a good score and show all your work, we will take the LaTeX file and give 20 points extra credit on that assignment.

Note: You may choose whether or not to attend class, and I aim to make class worth your time. If you do attend, I expect you to arrive on time and stay until the end.

Syllabus Statements

Classroom Behavior

Students and faculty are responsible for maintaining an appropriate learning environment in all instructional settings, whether in person, remote, or online. Failure to adhere to such behavioral standards may be subject to discipline. Professional courtesy and sensitivity are especially important with respect to individuals and topics dealing with race, color, national origin, sex, pregnancy, age, disability, creed, religion, sexual orientation, gender identity, gender expression, veteran status, political affiliation, or political philosophy.
For more information, see the classroom behavior policy, the Student Code of Conduct, and the Office of Institutional Equity and Compliance.

Requirements for Infectious Diseases

Members of the ���������� Boulder community and visitors to campus must follow university, department, and building health and safety requirements and all public health orders to reduce the risk of spreading infectious diseases.
The ���������� Boulder campus is currently mask optional. However, if masks are again required in classrooms, students who fail to adhere to masking requirements will be asked to leave class. Students who do not leave class when asked or who refuse to comply with these requirements will be referred to Student Conduct & Conflict Resolution. Students who require accommodation because a disability prevents them from fulfilling safety measures related to infectious disease will be asked to follow the steps in the “Accommodation for Disabilities” statement on this syllabus.

For those who feel ill and think you might have COVID-19 or if you have tested positive for COVID-19, please stay home and follow the further guidance of the Public Health Office. For those who have been in close contact with someone who has COVID-19 but do not have any symptoms and have not tested positive for COVID-19, you do not need to stay home.

Accommodation for Disabilities, Temporary Medical Conditions, and Medical Isolation

Disability Services determines accommodations based on documented disabilities in the academic environment. If you qualify for accommodations because of a disability, submit your accommodation letter from Disability Services to your faculty member in a timely manner so your needs can be addressed. Contact Disability Services at 303-492-8671 or
dsinfo@colorado.edu for further assistance.

If you have a temporary medical condition or required medical isolation for which you require accommodation, please let me know as soon as possible and we will work something out. Also see Temporary Medical Conditions on the Disability Services website.

Preferred Student Names and Pronouns

���������� Boulder recognizes that students' legal information doesn't always align with how they identify. Students may update their preferred names and pronouns via the student portal; those preferred names and pronouns are listed on instructors' class rosters. In the absence of such updates, the name that appears on the class roster is the student's legal name.

Honor Code

All students enrolled in a University of Colorado Boulder course are responsible for knowing and adhering to the Honor Code. Violations of the Honor Code may include but are not limited to: plagiarism (including use of paper writing services or technology [such as essay bots]), cheating, fabrication, lying, bribery, threat, unauthorized access to academic materials, clicker fraud, submiting the same or similar work in more than one course without permission from all course instructors involved, and aiding academic dishonesty.��

All incidents of academic misconduct will be reported to Student Conduct & Conflict Resolution: honor@colorado.edu, 303-492-5550. Students found responsible for violating the Honor Code will be assigned resolution outcomes from the Student Conduct & Conflict Resolution as well as be subject to academic sanctions from the faculty member. Visit Honor Code for more information on the academic integrity policy.