Math 630 (Practical) Advanced Linear Algebra

Fall 2003, Ed Bueler

Ed Bueler: felb@uaf.edu, x7693
Office: Chapman 301C (Hours)
Class time: MWF 10:30A - 11:30A  Classroom: Duckering 352
Text: Trefethen and Bau, Numerical Linear Algebra, SIAM Press 1997.
Syllabus and Advertisement

PARTS OF COURSE:
A
matrix/vector manipulations
B
geometric linear algebra
C
abstract linear algebra
D
QR factorization and least squares
E
conditioning and stability
F
systems of equations
G
computing eigenvalues
H
iterative methods

MATLAB CODES:
    ball.m
    clgs.m
    esgfit.m
    estnorm.m
    hello.m
    house.m
    mgs.m
    mylu.m
    myslash.m
    plotexpnorm.m
    polycos.m
    showmat.m
    showmat3D.m
    spectbvp.m
    svdhello.m
    testQR.m
    trichol.m

LINKS:
ON RESERVE IN RASMUSSEN (24 hour checkout):
  • Golub & van Loan, Matrix Computaions
  • Roman, Advanced Linear Algebra

 Schedule:  (my planning document, version 12/7/03, FINAL)

Part

Day

Lecture
(in text)
Topic
Assigned or Due
(links are PDF)
C
F 9/5

introduction, computing eigenvalues (by-hand vs. practical-for-big-matrices algorithm)
Assignment #1
C
M 9/8

abstract vector spaces, function spaces and finite dim'l subspaces

C, A
W 9/10
1
bases, linear maps, matrices, matrix product, matrix-vector multiplication
A#1 Due
Assign #2
C, A
F 9/12
1
cont.

A
M 9/15
9
intro to Matlab (in Chapman 103)

B
W 9/17
2
inner product, adjoint, hermitian, orthogonal, unitary

B
F 9/19
2
cont.

B
M 9/22
2
cont.

B
W 9/24
2,3
cont., norms of vectors
A #2 Due
B
F 9/26
3
norms of vectors and matrices
Assign #3

M 9/29
3, 4
norms, the singular value decomposition

B
W 10/1
4
more on the SVD

B
F 10/3
4, 5
more SVD
A #3 Due
B
M 10/6
4, 5
more SVD
Assign #4
B
W 10/8
4,5
more SVD, compression of images

B
F 10/10
6
projectors

B
M 10/13
6
cont
A #4 Due
D
W 10/15
7
Gram-Schmidt process and QR factorization

D
F 10/17
7
cont
Assign #5
D
M 10/20
8
modified Gram-Schmidt/operation count

D
W 10/22
10
Householder triangularization
A #5 Due
D
F 10/24
10
cont

D
M 10/27
11
Least squares (by QR, QVD and Cholesky)
Assign #6
D
W 10/29
11
cont


F 10/31

MIDTERM QUIZ: 1 HOUR in class
Review definitions and easy results in Lectures 1, 2, 3, 4, 5, 6, 7, 8, and 10.

Quiz

Solutions
D
M 11/3
11
Least squares cont

E
W 11/5
12
Conditioning
A #6 Due
E
F 11/7
12
Conditioning, cont

E
M 11/10
13
Floating point arithmetic
Assign #7
E
W 11/12
14, 15
Stability

E
F 11/14
14, 15
cont

E
M 11/17
16,17,19
Stability of: Householder, back sub, least squares

F
W 11/19
20
Gauss elimination
A #7 Due
F
F 11/21
20, 21
w. partial pivoting
Assign #8
F
M 11/24
22, 23
stability of Gauss elimination, Cholesky

B/C
W 11/26
24
Eigenvalues, Schur decomposition, spectral theorem

G
M 12/1
24
cont

G
W 12/3
24
cont
A #8 Due
G
F 12/5
24, 25
eigenvalue algorithms and power method
Final Exam (PDF)
G
M 12/8
25
cont

G
W 12/10
26
reduction to Hessenberg/tridiagonal;

G
F 12/12
28
QR for symmetric matrices


W 12/17

FINAL EXAM DUE at 12:15 at Ed's office or mailbox
FINAL EXAM DUE 12:15
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