Ed Bueler: felb@uaf.edu, x7693
Office: Chapman 301C ( Hours)
Class time: MWF 2:15--3:15pm Classroom:
Chapman 107
Text: Trefethen and Bau, Numerical Linear Algebra,
SIAM Press
1997.
Syllabus and Advertisement
A
|
matrix/vector manipulations
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B
|
geometric linear algebra
|
C
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abstract linear algebra
|
D
|
QR factorization
and least squares
|
E
|
conditioning and
stability
|
F
|
systems of equations
|
G
|
computing eigenvalues
|
H
|
iterative methods
|
MATLAB/Octave/Python CODES:
LINKS:
- Golub & van Loan, Matrix Computations
- Demmel, Applied Numerical Linear Algebra
- Higham, Accuracy and Stability of Numerical Algorithms
- Strang, Linear Algebra and Its Applications
- Roman, Advanced Linear Algebra
- Moler, Numerical Computing with MATLAB
- Cheney & Kincaid, Numerical Mathematics and
Computing
- Press et al, Numerical Recipes in C|Fortran
|
Schedule: (version 5/9/09)
Part
|
Day
|
Lecture
(in text)
|
Topic
|
Assigned or Due
(links are PDF)
|
C
|
1/23 Fri
|
|
introduction, matrices, vector spaces and
examples
|
A #1 (includes
proof advice) (PDF)
Matlab/Octave/Pylab comparison
handout (PDF)
|
C
|
1/26 Mon
|
1
|
bases, linear maps, matrices |
|
C, A
|
1/28 Wed
|
1
|
matrix-vector multiplication,
matrix product |
|
C, A
|
1/30 Fri
|
2
|
inner product, adjoint,
hermitian, orthogonal, unitary |
A
# 1 Due
A #1 solutions (PDF)
A #2 (PDF)
|
A
|
2/2 Mon
|
2
|
cont.
|
|
B
|
2/4 Wed
|
2
|
cont.
|
|
B
|
2/6 Fri
|
3
|
norms of vectors and matrices |
|
B
|
2/9 Mon
|
3
|
cont.
|
A
# 2 Due |
B
|
2/11 Wed
|
4
|
the singular value decomposition |
A #3 (PDF) |
B
|
2/13 Fri
|
4
|
cont
|
|
B
|
2/16 Mon
|
5
|
cont
|
|
B
|
2/18 Wed
|
5
|
compression of images |
A
# 3 Due |
B
|
2/20 Fri
|
6
|
projectors |
A #4
(PDF) |
B
|
2/23 Mon
|
6
|
cont
|
|
B
|
2/25 Wed
|
6
|
cont
|
|
D
|
2/27 Fri
|
7
|
Gram-Schmidt process and QR
factorization |
A
# 4 Due
REVISED A #5
(PDF)
|
D
|
3/2 Mon
|
8
|
modified
Gram-Schmidt/operation count |
|
D
|
3/4 Wed
|
10
|
Householder triangularization |
|
D
|
3/6 Fri
|
10,11
|
cont; least squares |
|
D
|
3/9-3/13
|
|
SPRING BREAK
|
|
D
|
3/16 Mon
|
11
|
least squares (by QR, QVD and Cholesky) |
A
# 5 Due |
E
|
3/18 Wed
|
12
|
conditioning
|
A #6
(PDF) |
E
|
3/20 Fri
|
12
|
cont
|
|
E
|
3/23 Mon
|
13
|
floating point arithmetic
|
review notes
(PDF) |
|
3/25 Wed
|
|
MIDTERM
QUIZ: Wednesday in class
|
quiz
itself
solutions
|
E
|
3/27 Fri
|
13
|
cont
|
|
E
|
3/30 Mon
|
14
|
stability and backward
stability |
A
# 6 Due |
E
|
4/1 Wed
|
15
|
cont
|
|
E
|
4/3 Fri
|
16,17,19 |
stability of: Householder,
back sub, least
squares |
A #7
(PDF) |
E
|
4/6 Mon
|
|
cont
|
|
F
|
4/8 Wed
|
20
|
Gauss elimination |
|
F
|
4/10 Fri
|
21
|
w. partial pivoting
in class example: partialpivot_lu.txt
|
A
# 7 Due |
F
|
4/13 Mon
|
22, 23 |
stability of Gauss elimination, Cholesky
in class example: bad_lu.txt
|
|
F
|
4/15 Wed
|
|
cont
|
A #8
(PDF) |
G
|
4/17 Fri
|
24
|
eigenvalues, Schur decomposition, spectral
theorem |
|
G
|
4/20 Mon |
|
cont
|
|
G
|
4/22 Wed
|
25
|
eigenvalue algorithms
|
|
G
|
4/24 Fri
|
|
springfest, no class
|
|
G
|
4/27 Mon |
26
|
reduction to Hessenberg/tridiagonal
[see in-class codes in list at left]
|
A
# 8 Due |
H
|
4/29 Wed
|
28
|
inverse and Rayleigh iteration for
eigenvalues of matrices |
FINAL EXAM
(PDF) |
H
|
5/1 Fri
|
|
Krylov ideas: how to solve really large Ax=b
|
|
H
|
5/4 Mon |
|
|
|
|
5/7 Thurs
|
|
FINAL EXAM
(PDF)
take
home; due Thursday May 7, 5pm at my office box
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|
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