Simon Fraser University
Engaging the World

Course Outlines

Fall 2024 - APMA 920 G100

Numerical Linear Algebra (4)

Class Number: 3877

Delivery Method: In Person

Overview

  • Course Times + Location:

    Sep 4 – Oct 11, 2024: Tue, Thu, 2:30–4:20 p.m.
    Burnaby

    Oct 16 – Dec 3, 2024: Tue, Thu, 2:30–4:20 p.m.
    Burnaby

Description

CALENDAR DESCRIPTION:

Conditioning and stability of numerical methods for the solution of linear systems, direct factorization and iterative methods, least squares, and eigenvalue problems. Applications and mathematical software.

COURSE DETAILS:

This is a foundational course in which you will be introduced to core ideas in numerical linear algebra: how to factor matrices to reveal important structure, computing solutions of least squares problems and uncovering spectral properties.  Linear algebra - and numerical algorithms for linear algebra - is very important in data science. We will see applications to data science during the course. I also intend to spend roughly the last quarter of the class on randomized numerical linear algebra techniques, which have developed in the last 15 years to tackle problems in big data.

Syllabus:

  • Linear Algebra Review
  • The Singular Value Decomposition
  • QR Factorization
  • Conditioning and Stability
  • Least Squares Problems
  • Linear Systems
  • Computing Eigenvalues
  • Iterative Methods
  • Randomized Numerical Linear Algebra and Big Data

Grading

  • Homework 50%
  • Quizses (2 in total) 10%
  • Final Exam 40%

REQUIREMENTS:

Prerequisites:

Undergraduate courses in Linear Algebra and Numerical Analysis. Programming experience. Any code distributed by the instructor will be written in Matlab.

Materials

REQUIRED READING:

Numerical Linear Algebra, Trefethen & Bau, SIAM 1997
ISBN: 0898713617

REQUIRED READING NOTES:

Your personalized Course Material list, including digital and physical textbooks, are available through the SFU Bookstore website by simply entering your Computing ID at: shop.sfu.ca/course-materials/my-personalized-course-materials.

Graduate Studies Notes:

Important dates and deadlines for graduate students are found here: http://www.sfu.ca/dean-gradstudies/current/important_dates/guidelines.html. The deadline to drop a course with a 100% refund is the end of week 2. The deadline to drop with no notation on your transcript is the end of week 3.

Registrar Notes:

ACADEMIC INTEGRITY: YOUR WORK, YOUR SUCCESS

SFU’s Academic Integrity website http://www.sfu.ca/students/academicintegrity.html is filled with information on what is meant by academic dishonesty, where you can find resources to help with your studies and the consequences of cheating. Check out the site for more information and videos that help explain the issues in plain English.

Each student is responsible for his or her conduct as it affects the university community. Academic dishonesty, in whatever form, is ultimately destructive of the values of the university. Furthermore, it is unfair and discouraging to the majority of students who pursue their studies honestly. Scholarly integrity is required of all members of the university. http://www.sfu.ca/policies/gazette/student/s10-01.html

RELIGIOUS ACCOMMODATION

Students with a faith background who may need accommodations during the term are encouraged to assess their needs as soon as possible and review the Multifaith religious accommodations website. The page outlines ways they begin working toward an accommodation and ensure solutions can be reached in a timely fashion.