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Numerical Algebra
This course consists of two parts:
- Scientific Computation Computational Algebra
(SCCA) is given in September-October. It is included in the
International Masters program in Scientific Computation, but is open
for anybody with a basic course in Numerical Analysis. It gives 3 hp.
- Methods for Large Matrices, is normally given in
October-December. In Fall 2007 it will not be given, but it will come
back Fall 2008 with Michael Hanke as instructor.
Scientific Computation Computational Algebra 2007
Sign up for the course in the res system: signup.html
If you are not yet registered, please sign up at
your earliest convenience!
If you do not have a Swedish personnummer,
use a temporary number from KTH or after your own choice. It should have
digits and the letter A. First six digits are yymmdd of your birthday,
last four Ad1d2d3. The second last digit d2 should be odd for men and even
for women. We hope that no people with the same birtday choose the same
lucky number.
Instructors
Axel Ruhe , room D
4527, Phone 6635: Lectures, Examiner
Mohammad Motamed,
room D 4519, Phone 7142: Lab sessions, Advisor
News:
- September 7: Demmel books ordered for those on list.
- September 11: Lab 1 today. Change
text in labs distributed on Sept 5: Assignment 4 matrix B, first line
should be '1 2 3 4 5' instead of '11 12 13 14 15'! You will get nicer
results that way, INF instead of a large number.
- September 24: FAQ set up concerning labs
- October 3: Pr ogr assignment 1 graded. Returned at lecture Oct 4.
- Extra Lab session scheduled on October 17 at 10-12
- October 10: Lab 3 should be handed in by October 18! Give it to Mohammad or Axel or put it in letter box at Studentexpeditionen.
- For all lab reports: Write on top left on first page
1. your name and personal number, one line for each responsible person,
2. next line course code: DN2251 teacher: Axel Ruhe,
- Exams are graded now, November 1.
- Exams and labs will be shown November 5, Monday at 15:15 in D4523! It
has been difficult to find results in the res system. All those of you
that signed in via the web page did not get your user names in and then
the system did not recognise your identity. I will answer questions on
results by email if you cannot come on Monday.
- The
grades are computed the following way: The course DN2251 is worth 9 hp,
högskolepoäng. Of this Computational Algebra is 3 hp and
Differential equations 6 hp. We grade the labs up to 6 each and the
exam 18, 2 for each question, total up to 36. To pass the course you
must have submitted all 3 labs and taken the exam with at least 9. If
you pass you get a grade,
Grade |
Points |
people |
A |
31 |
7 |
B |
27 |
8 |
C |
25 |
4 |
not yet passed |
|
10 |
- If your exam needs passing, a new exam is given Saturday January 19 2008 at 10-13 in room D41
Plan for lectures 2007
Lectures, Föreläsningar, F1-F6 are given in various lecture halls around campus. Look carefully at your maps!
Lab sessions, L1-L6, are held in rooms Grå and Karmosin in the main building E, western wing 5 th floor.
New
times for labs that are separate from Differential equations course DN2225.
Meeting
|
Preparation
|
Text
|
Contents
|
F1, Sept 5 10:15-12 in M3
|
1.2, 1.3
|
L 1
D 1.2-3
D 2.1-4
|
Introduction: General concepts in
numerical linear algebra. The standard problems.
Linear systems: Gaussian elimination and factorizations, pivoting,
error analysis
|
L1, Sept 11 15-17
|
|
|
1. Floating point arithmetic, Gaussian
elimination: Lab 1 distributed
|
F2, Sept 13 13:15-15 in V2
|
|
|
Linear systems, continued
|
L2, Sept 18 15-17
|
|
|
Work on lab 1
|
F3, Sept 19 10:15-12 in M2
|
2.1, 2.3, 2.4, 5.1
|
L 2
D 2.7
|
Sparse matrices: Direct methods for linear
systems
|
L3, Sept 25 15-17
|
|
|
2. Sparse matrices: Lab 2 distributed
lab072.html
|
F4 Sept 27 10:15-12 in M3
|
2.5, 5.2
|
L 3
D 3.1-2 3.5
|
Least squares: Theory, normal equations,
singular value decomposition (SVD), numerical rank
|
L4, Sept 28 8-10
|
|
|
Work on lab 2
|
F5, Oct 4 10:15-12 in D34
|
1.5,
|
L 4
D 4
|
Eigenvalues: Theory, perturbation
analysis, Transformation algorithms
|
L5, Oct 5 8-10
|
|
|
3. SVD for data analysis: Lab 3 distributed. Data needed for pattern recognition exercise zipdata.mat ima2.m
|
F6, Oct 11 10:15-12 in E2
|
5.3
|
L 5
D 6.6
|
Very large matrices: Iterative
algorithms
|
L6, Oct 11 15-17
|
|
|
Work on lab 3
|
L extra 7, Oct 17 10-12 in Grå and Karmosin |
|
|
Make lab 3 ready! |
Preparation: Texts from
Strang Applied Mathematics , the course book of
DN2266.
Text: Lc Text in lecture notes chapter c. D c.s Demmel
text book Chapter c section s.
Contents: What is discussed in this lecture.
Assignments: Computing lab assignments given out this week.
Text book
Most of the course is in the book: James W. Demmel,
Applied
Numerical Linear Algebra, SIAM 1997, Order code OT56,
homepage
It has been difficult to get the book in Stockholm. There
is a way to buy it directly from the publisher, who offers a discount
for members. SIAM offers a free student membership to students of SIAM
member schools of which one is Royal Institute of Technology, KTH. Sign
in at
SIAM:
Students
You may follow the first part of the course, 3 hp, without the
book, but if you intend to follow the second, 6 hp, you are
recommended to get the book.
Lecture notes
Topics in Numerical Linear Algebra, copies distributed at lecture: Linalgtop.pdf
Review questions used to prepare for exam distributed:
RevQ.pdf
Examination
The grading of the course is based on the 3 programming assignments and
a written exam with questions covering the theory part of the course. See
FAQ concerning the programming assignments!