KTH / CSC / Kurser / 2D1252 / numalg07

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!