Math 614 Numerical Linear Algebra

Fall 2021, UAF

Ed Bueler
elbueler@alaska.edu

Office: Chapman 306C (hours)

Sections:
in person:   F01, crn 74997
online:   FXA, crn 75737

Canvas course page:
https://canvas.alaska.edu/courses/2362
(Go here for the Zoom and Discord links.)

Class times and room:
MWF 10:30--11:30am
Chapman 206  107 (or web-based)

Syllabus

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Parts of the course:

A
matrix mechanics & vector spaces
B
geometric linear algebra
C
SVD
D
QR & least squares
E
conditioning & stability
F
systems of equations
G
computing eigenvalues
H
iterative methods


Required text: L. Trefethen and D. Bau, Numerical Linear Algebra, SIAM Press 1997. (at UAF bookstore or $74 at bookstore.siam.org)

Four other texts are recommended. The first is a great Matlab tutorial (and free online). The second is a possible online text for this course; it is free online and has linked videos. The third is a standard reference for numerical linear algebra. The fourth is helpful when doing research in this area.
Matlab/Octave codes:

a few Python codes:

Links:

Schedule: (version 19 October 2021)

Part Day Lecture Topic
• Materials
Due or Exam
• Assigned
A Mon 8/23 1 matrix/vector thinking
A Wed 8/25 vector spaces, bases
A Fri 8/27 intro to Matlab/Octave
B Mon 8/30 2 inner products and orthogonality A #1 DUE
B Wed 9/1 3 norms of vectors and matrices A #1 DUE
B Fri 9/3 cont.
Mon 9/6 no class: Labor Day no class
B Wed 9/8 cont.
C Fri 9/10 4 singular value decomposition (SVD) A #2 DUE
C Mon 9/13 5 applications of SVD
C Wed 9/15 SVD existence theorem
C Fri 9/17 by-hand calculation of SVD A #3 DUE
C Mon 9/20 image compression
principal component analysis (PCA)
D Wed 9/22 6 projectors
D Fri 9/24 cont.
D Mon 9/27 7 Gram-Schmidt process and QR factorization A #4 DUE
D Wed 9/29 8 modified Gram-Schmidt/operation count
D Fri 10/1 Quarterterm Quiz
in class (F01) or proctored (FXA)
30 minutes
Quarterterm Quiz
D Mon 10/4 10 Householder reflections
D Wed 10/6 11 least squares (QR, SVD, normal eqns)
D Fri 10/8 cont.
D Mon 10/11 cont. A #5 DUE
E Wed 10/13 12 conditioning of problems
E Fri 10/15 cont.
Midterm Exam
E Mon 10/18 13 floating point arithmetic
A #6 DUE
E Wed 10/20 14 backward stability of algorithms
Fri 10/22 Midterm Exam
in class (F01) or proctored (FXA)
RESCHEDULED!
Midterm Exam
E Mon 10/25 cont.
E Wed 10/27 15 theorem: backward-stable algorithms are safe on well-conditioned problems
E Fri 10/29 16 backward stability of Householder QR
E Mon 11/1 17 backward stability of back-substitution A #7 DUE
F Wed 11/3 20 Gauss elimination as LU
F Fri 11/5 21 LU with w. partial pivoting
F Mon 11/8 cont.
F Wed 11/10 22 stability of LU
F Fri 11/12 23 Cholesky decomposition
G Mon 11/15 24 eigenvalues
G Wed 11/17 25 computing eigenvalues
G Fri 11/19 26, 27, 28 summary: QR algorithm for eigenvalues
G Mon 11/22 cont.
Wed 11/24 no class: Thanksgiving no class
Fri 11/26 no class: Thanksgiving no class
H Mon 11/29 32 iterative methods: overview
H Wed 12/1 33 Arnoldi iteration release of Final Exam
H Fri 12/3 35 GMRES
Mon 12/6 no class: study for Final Exam no class
Wed 12/8 Final Exam
take-home exam due 5 pm
Final Exam