CSCI 554: Matrix Computation (Winter 2022)

Course Description

Through the use of lectures, discussions, the text, assignments, and labs, this course will familiarize students with the advanced knowledge of triangular systems, positive definite systems, banded systems, sparse positive definite systems, general systems; Sensitivity of linear systems; orthogonal matrices and least squares; singular value decomposition; eigenvalues and eigenvectors; and QR algorithm with their applications.

See the course outline for more information.

Course Details

Lecture Time/Place

Tuesday, 3:15pm–4:05pm; Thursday, 2:15pm–3:05pm; Friday, 4:15pm–5:05pm

All lectures are held in Mulroney Hall, room 3026.

Textbook

G. H. Golub and C. F. Van Loan, Matrix Computations. Johns Hopkins University Press, 4th edition, 2013.

The textbook is not required, but is useful as a secondary reference. Course notes will also be provided for each lecture.

Marking Scheme

You must complete both the written report component and the presentation on the report in order to pass the course, even if the weighted sum of your other submissions is at least 50%. You may not complete one without completing the other.

News

Lectures

Week Notes Readings
1 Introduction: matrix multiplication Golub & Van Loan, 1.1–1.3
2 Review of linear algebra: systems of linear equations Golub & Van Loan, 2.1, 3.1
3 Gaussian elimination and LU decomposition Golub & Van Loan, 3.1–3.2
4 Sensitivity and error Golub & Van Loan, 2.2–2.3, 2.6
5 Least squares: QR decomposition Golub & Van Loan, 5.1–5.2
Winter study break
6 Least squares (cont’d): Gram–Schmidt process Golub & Van Loan, 5.2–5.3
7 Singular value decomposition Golub & Van Loan, 2.4, 5.4–5.5
8 Eigenvalues and eigenvectors: power method Golub & Van Loan, 7.1, 7.3
9 Eigenvalues and eigenvectors (cont’d): QR algorithm Golub & Van Loan, 7.4–7.5
10 Student presentations
11 Student presentations
12 Student presentations

Code

For some algorithms presented in the lecture notes, an associated Python code file is included below to implement the algorithm. This code is not guaranteed to be the most efficient or most beautiful code, so feel free to modify it, experiment with it, and improve it.

Assignments

Assignments are due at the beginning of class on the due date. Late assignments will be accepted up to the beginning of the first class following the due date. Late assignments are subject to a penalty of 10% deducted from the earned mark.

The written report and presentation must be submitted on the due date. Late submissions will not be accepted.

Personnel

Instructor

Taylor J. Smith
Email: tjsmith [at] stfx [dot] ca
Office: Annex, Room 9A
Student hours: Monday, 9:15am–11:15am