Math 630 - Numerical Linear Algebra

Spring 2021 - Matthias K. Gobbert

Detailed Schedule - Last Updated April 19, 2021

The synchronous class meetings are online, on Tuesdays and Thursdays 04:00-05:15, in Blackboard Collaborate. Please, see the detailed schedule below for more information.
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 HW00, HW01, HW02, 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" due before that class.
The numbers GQ0a, GQ1a, GQ2a, etc. in the Main Topic column indicate in-class group quizzes "GQ" during that class due as PDF upload.
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	Time / Main Topic	Section(s) / Room
1, HW0	Tu 01/26	BQ0a, BQ0b, IQ0, Overview, GQ0a
2, HW1	Th 01/28	Gaussian elimination without row interchanges, GQ1a	1.7
3	Tu 02/02	Gaussian Elimination (GE) and the LU Decomposition, GQ1b	1.8
4, HW2	Th 02/04	Roundoff Errors; Propagation of Roundoff Errors	2.5, 2.6
5	Tu 02/09	Operation count for GE, pivoting, and triangular solves, GQ1c
6, HW3	Th 02/11	Vector Norms	2.1
7	Tu 02/16	Matrix Norms, GQ1d	2.1
8, HW4	Th 02/18	Sensitivity Analysis and Condition Numbers	2.2, 2.3
9	Tu 02/23	A Posteriori Error Analysis; Backward Error Analysis of GE, GQ1e	2.4, 2.7
10, HW5	Th 02/25	Positive Definite Systems; Cholesky Decomposition; Sparse GE and Cholesky in Matlab	1.4, 1.6, 1.9
11	Tu 03/02	Iterative Methods for Linear Systems; A Model Problem	8.1
12, HW6	Th 03/04	The Classical Iterative Methods	8.2
13	Tu 03/09	Steepest Descent for linear systems, GQ2a	8.4, 8.7
14, HW7	Th 03/11	The CG Method, preconditioning, GQ2b	8.7, 8.6, 8.10
	Tu 03/16	Spring Break
	Th 03/18	Spring Break
15	Tu 03/23	Theory of classical iterative methods and the CG method, GQ2c	8.3, 8.8, 8.9
16, HW8	Th 03/25	Review
17	Tu 03/30	Review of eigenvalues and diagonalization	5.2
18, HW9	Th 04/01	Midterm Exam
19, HW10	Tu 04/06	Review of diagonalization, complex matrices, notation, and motivation of QR factorization, GQ3a	5.4
20	Th 04/08	The discrete least squares problem and the QR factorization	3.1-3.2
21, HW11	Tu 04/13	QR factorization and least squares problems	3.2-3.3
22	Th 04/15	The Singular Value Decomposition (SVD)	4.1
23	Tu 04/20	Properties of the SVD	4.2
24, HW12	Th 04/22	The SVD and the Least Squares Problem	4.3
25	Tu 04/27	The Power Method and Extensions	5.3
26	Th 04/29	Similarity transformation; reduction to Hessenberg form; the QR Algorithm	5.5
27, HW13	Tu 05/04	Shifts in the QR Algorithm	5.6
28, HW14	Th 05/06	Computer numbers: IEEE-standard for floating-point numbers
29, HW15	Tu 05/11	Review
	Tu 05/18	03:30-05:30 Final Exam Note the date and time!