Math 630 - Numerical Linear Algebra

Spring 2024 - Matthias K. Gobbert

Detailed Schedule - Last Updated 03/15/2024

This schedule is designed to give you an overview of the material to be covered and is tentative in nature. It is a living document and will be updated throughout the semester.
The section numbers refer to David S. Watkins, Fundamentals of Matrix Computations, third edition, Wiley, 2010.
The numbers HW0, HW1, HW2, etc. in the Class column indicate homeworks "HW" due as PDF upload to Blackboard on that day.
The numbers IQ0, BQ0a, BQ0b, etc. in the Main Topic column indicate online Blackboard quizzes "IQ" and "BQ".
The numbers GQ0a, GQ1a, GQ1b, etc. in the Main Topic column indicate in-class group quizzes "GQ" during that class.
These numbers in the detailed schedule are designed to show the teaching philosophy and learning techniques associated with each class meeting.
See the Assignments area of the Blackboard site for our course for the precise due dates and times.

Class	Date	Main Topic	Section(s)
1, HW0	M 01/29	BQ0a, BQ0b, IQ0, Overview, GQ0a, pre-assessment
2, HW1	W 01/31	Gaussian elimination without row interchanges, GQ1a	1.7
3	M 02/05	Gaussian Elimination (GE) and the LU Decomposition, GQ1b	1.8
4, HW2	W 02/07	Roundoff Errors; Propagation of Roundoff Errors	2.5, 2.6
5	M 02/12	Operation count for GE, pivoting, and triangular solves
6, HW3	W 02/14	Vector Norms	2.1
7	M 02/19	Matrix Norms, GQ1d	2.1
8, HW4	W 02/21	Sensitivity Analysis and Condition Numbers	2.2, 2.3
9	M 02/26	A Posteriori Error Analysis; Backward Error Analysis of GE, GQ1e	2.4, 2.7
10, HW5	W 02/28	Positive Definite Systems; Cholesky Decomposition; Sparse GE and Cholesky in Matlab	1.4, 1.6, 1.9
11	M 03/04	Iterative Methods for Linear Systems; A Model Problem	8.1
12, HW6	W 03/06	The Classical Iterative Methods	8.2
13	M 03/11	Steepest Descent for linear systems, GQ2a	8.4, 8.7
14, HW7	W 03/13	The CG Method, preconditioning, GQ2b	8.7, 8.6, 8.10
	M 03/18	Spring Break
	W 03/20	Spring Break
15	M 03/25	Theory of classical iterative methods and the CG method	8.3, 8.8, 8.9
16, HW8	W 03/27	Derivation and convergence of the CG Algorithm, GQ2c	8.8, 8.9
17, HW9	M 04/01	Review of eigenvalues and diagonalization, GQ2d	5.2
18	W 04/03	Midterm Exam
19, HW10	M 04/08	Diagonalization, complex matrices, notation, and motivation of QR factorization, GQ3a	5.4
20	W 04/10	The discrete least squares problem and the QR factorization	3.1-3.2
21, HW11	M 04/15	QR factorization and least squares problems	3.2-3.3
22	W 04/17	The Singular Value Decomposition (SVD)	4.1
23	M 04/22	Properties of the SVD	4.2
24, HW12	W 04/24	The SVD and the Least Squares Problem	4.3
25	M 04/29	The Power Method and Extensions	5.3
26, HW13	W 05/01	Similarity transformation; reduction to Hessenberg form; the QR Algorithm	5.5
27	M 05/06	Shifts in the QR Algorithm	5.6
28, HW14	W 05/08	Computer numbers: IEEE-standard for floating-point numbers
29, HW15	M 05/13	Review, post-assessment
	M 05/20	03:30-05:30 Final Exam Note the date and time!