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# Numerical Algebra

## Course news, autumn 2008

• Here you will find some sample examinations: exam0601.pdf, exam0710.pdf.
• Sara has scheduled questioning hours now: Tuesdays 15-16.
• The written examination is now scheduled: It will take place in rooms D35, D42 on October 24, 2008, 9-12.
• When using matlab's IDE on Solaris machines the caret sign (^) is not immediately available. For making it available to matlab issue the command
``` xmodmap -e "keycode 55 = SunFA_Diaeresis asciicircum asciitilde"
```
before you start matlab. Then, the caret key should work fine.
• The course starts in lecture hall B3 on Wednesday September 3, 2008 at 10.00 o'clock.

## Scientific Computation Computational Algebra 2008

### Instructors

Michael Hanke, room D4529, phone 08-7906278: Lectures, Examiner
Sara Zahedi, room D4519, phone 08-790 7142: lab sessions, advisor. Questioning hours: Tuesdays 15-16

### Plan for lectures 2008

Lectures, Föreläsningar, F1-F6 are given in various lecture halls around campus. Look carefully at your maps!
Lab sessions, L1-L5, are held in rooms Grå, Karmosin, and Orange in the main building E, western wing 5 th floor. The exception is L6 which will be held in Spelhallen och Sporthallen.
 Meeting Preparation Text Contents F1, Sept 3 10:15-12  in B3 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 4 13-15 in Orange 1. Floating point arithmetic, Gaussian elimination: Lab 1 distributed F2, Sept 10 10:15-12 in V2 Linear systems, continued L2, Sept 11 15-17 in Grå, Karmosin Work on lab 1 F3, Sept 23 10:15-12 in B3 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 in Grå, Karmosin 2. Sparse matrices: Lab 2 distributed F4 Sept 30 8:15-10 in D2 2.5, 5.2 L 3 D 3.1-2 3.5 Least squares: Theory, normal equations, singular value decomposition (SVD), numerical rank L4, Oct 2 15-17 in Grå, Karmosin Work on lab 2 F5, Oct 7 8:15-10 in L1 1.5, L 4 D 4 Eigenvalues: Theory, perturbation analysis, Transformation algorithms, L5,  Oct 9 15-17 in Grå, Karmosin 3. SVD for data analysis: Lab 3 distributed F6, Oct 14 8:15-10 in K2 5.3 L 5 D 6.6 Very large matrices: Iterative algorithms L6, Oct 16 10-12 in Spel, Sport Work on lab 3

Preparation: Texts from Strang Applied Mathematics.
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.

### Computer lab assignments

The laboratory work consists of three assignments carried out by groups of no more than two students. Each group hands in a report on each assignment in the NADA mailbox outside the Students' expedition (NOT the instructors' mail stops!), according to the schedule below. Attach a cover page properly filled in. It can be downloaded here or fetched at the Student Expedition. We strongly prefer paper hand-ins, the Swedish post office can be relied upon for those unable to attend in person. Homework is handed back in the Student Expedition.

The assignment reports should be clearly written and easy to read for the grader. If you use a computer, you must edit the output and write a descriptive summary. Mere sheaves of computer plots and printed output will not be accepted. Here are some guidelines how a report should be prepared. A good example of a nice report can be found here.

Here are the references to the computer labs:

• Lab 1, due September 25, 2008
• Lab 2, due October 9, 2008. Extra tips on sparse matrices in matlab can be found here. The detailed description of the implementation is given in gilbert92sparse.pdf.
• Lab 3, due October 27, 2008. The following files are needed for the assignment: zipdata.mat, ima2.m
See the FAQ concerning the programming assignments!

### 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, 7.5 hp, you are recommended to get the book.

### Lecture notes

Axel Ruhe: Topics in Linear Algebra. Sold at the students' expedition
Review questions used to prepare for exam will be distributed: RevQ.pdf

### Examination

The grading of this part of the course is based on the three programming assignments and a written examn with questions covering the theory part of the course.

This part of the courses DN2251/2 Computational Algebra is 3 ECTS. We grade the labs up to 6 each and the exam 18, 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 according to the accumulated number of points. So grade E corresponds to at least 12 points.