Philosophy

Course description:
In this class we are going to explore a wide array of computational methods related to linear algebra problems and optimization. There will be a lot of Matlab coding and hands-on exploration of properties through experiments and rigorous mathematical argumentation.




The schedule
Check often for updates, links and what not. Exercises and concepts marked in italics are more difficult. Take special care to understand the difficult concepts. Beyond the current week, DATES for assignments are tentative

Week	Lecture		Section	Description and problems
1	02/10	M		Working out an algorithm (slides for week 1)
	02/12	W		Experiments and theory on Monday's algorithm
	02/14	F		A translation exercise DUE FOR MONDAY. Read Lectures 1 and 2 from the book
2	02/17	M	L3	Norms (slides for week 2)
	02/19	W	L4, L5	The Singular Value Decomposition. HW1
	02/21	F		Two applications: the pseudoinverse and spectral compression
3	02/24	M	L6	Projectors (slides for week 3)
	02/26	W	L7	QR factorizations. HW1 due
	02/28	F		Work-n-code day. Exploring Householder matrices (working document) FOR NEXT WEEK. Read Lecture 8 and 9. Coding assignment #1
4	03/03	M		Class canceled due to inclement weather
	03/05	W	L8, L10	More QR factorizations (slides for week 4)
	03/07	F	L11	Least squares. HW2 Coding assignment #1 due
5	03/10	M	L12	Conditioning (slides for week 5)
	03/12	W	L13, L14	Floating point and backward stability of algorithms
	03/14	F	L15	Conditioning and stability + More Matlab 4U. (The Matlab code of today's lecture) HW2 due Coding assignment #2
	03/17	M	L17	Back substitution (slides for week 6)
	03/19	W	L16	Stability of Householder triangularization
	03/21	F	L20, 21	Gaussian elimination Coding assignment #2 due
7	03/24	M		Exam #1. In-class part (fast rounds)
	03/26	W		Work on your exam
	03/28	F		Problems
8	SPRING BREAK
9	04/07	M	L22	The Cholesky factorization (slides for week 9) HW3
	04/09	W	L32	Classical ideas on iterative methods
	04/11	F	L33	Krylov subspaces and the Arnoldi iteration
10	04/14	M	L34, 35	GMRES (slides for week 10) Coding assignment #3 HW3 due
	04/16	W	L35, 36	Lanczos
	04/18	F	L38	CG and preconditioned CG
11	04/21	M		Unconstrained minimization (slides for week 11) HW4 Coding assignment #3 due
	04/23	W		Convexity
	04/25	F		Steepest descent and Newton descent
12	04/28	M		Convex sets (slides for week 12) HW4 due
	04/30	W		Linear programming
	05/02	F		Problems (in-class coding assignment #4)
13	05/05	M		Convex functions on convex sets (slides for week 13) HW5
	05/07	W		Problems
	05/09	F		Lagrange multipliers and Kuhn-Tucker conditions
14	05/12	M		Work-n-code day (Nelder-Mead method) HW5 due
	05/14	W		Exam #2. In-class part
	05/16	F		Discussion on exam and more coding
15	05/19	M		Coding assignment #5 due