General information

Numerical Linear Algebra ENM-TMA265 and GU-MMA600 7.5 credit points
New deadlines for homeworks and computer exercises, see section Programme
All students should register for this course. Registration is still open until 8 September, see
Obs! Participation at least 50% of lectures at this course is necessary!
23.09.2014: I'm check your homeworks and comp.ex. 1. Results will be announced in the form of "List of bonuspoints" at the next week, latest at Friday. Obs! It was not possible to move examination. So, examination will be at 31 October, 14.00-18.00.
24.09.2014: Now list of bonuspoints for homework 1 is done.
26.09.2014: List of bonuspoints for comp.ex. 1 is done.
01.10.2014: List of bonuspoints for homework 2 is done.
09.10.2014: I put matlab program in Computer Labs to present contour plot of eigenvectors for Poisson's equation. This is useful program for comp.ex.5.
15.10.2014: New list of bonuspoints is done.
16.10.2014: Deadline is postponed to Monday, 20.10.2014. Also examination at 31.10.2014 is moved from Väg och vatten to Maskinhuset.
22.10.2014: Now final list of bonuspoints is done. If I have missed something - please, sent me mail with your homeworks or computer exercises. I will add these bonusponts to your examination grades. Examination is at 31 October and is moved from Väg och vatten to Maskinhuset. It is allowed to use on the examination notes written on the one side of A4-page. After 1 November I will put answers to the questions to "Examination". When I will check all examinations - I will inform about it on this page. Then ask personal in expedition about your grades. Good luck on examination!
  • All examination works written at 31.10.2014 (well done!) are verified and you can get information about your grades at expedition. Ask personal at expedition about information in LADOK.
  • Answers to the questions at examination are here:
  • Answers for examination at 31.10.2014
  • Examination written at 03.01.2015 is verified and You can get information about Your grades at expedition. Ask personal at expedition about information in LADOK.
  • Answers for examination at 03.01.2015
  • I also thank all of You who have answered to the following course evaluation survey:
  • Course evaluation survey
  • This survey helps me get feedback from You and improve course for the next time. Thus of You who have not yet filled it: I will be very grateful if You can fill it. You can sent this survey by mail or put it in the red box before my office. Thank You!


    Numerical linear algebra problems arise in many different fields of science like computational fluid dynamics, solid mechanics, electrical networks, signal analysis, and optimisation. In this course we study basic linear algebra concepts like matrix algebra, theory for linear systems of equations, spectral theory, and vector- and matrix norms as well as numerical aspects like efficiency, reliability, error analysis and condition numbers. We consider three linear algebra building bricks in computation:

    For all three building bricks above we discuss numerical algorithms with respect to applicability, reliability, accuracy, and efficiency. By computer exercises the students get experiences in implementation and evaluation of numerical algorithms for linear algebra problems.

    By the completion of this course the students will be able to:

    The course consists of 36 lecture hours, 20 exercise hours and gives 7.5 points. The course code for engineering schools and students registered at Chalmers is TMA265. The course code for students registered in GU is MMA600.
    Latest news
    All current and recent information will be placed here. Regarding examination : CTH students should not register for this exam. Only GU students can register for the examination. CTH and GU students will get their personal exam numbers from Observers of this exam. Examination usually is at Maskinhuset at Chalmers:
  • Maskinhuset
  • Where exactly (in which one room) will be exam You will know at the day of examination: the announcement will be placed at the blackboard close to the entree of Maskinhuset. Notes: GU students can do re-examination but they can not high their scores (for example, from G to VG) but Chalmers students can do re-examination and high scores. Please, follow this site to get exact information when and where will be re-examonation closer to the day of re-examination.
    The schedule for the course can be found via the link to webTimeEdit top of the page.

    Day Time Place Remarks Office Hours
    MON 13-15 MVF33 Lecture
    WED 13-15 MVF24 Computer exercises
    THU 10-12 MVF33 Lecture
    FRI 13-15 MVF24 Computer exercises
    31.10.2014 14.00-18.00 Maskinhuset Examination
    03.01.2015 14.00-18.00 Maskinhuset Examination
    Link to the system ping pong:
  • Ping Pong
  • Teachers
    Course coordinator: Larisa Beilina,, room 2089, homepage

    Course literature
    1. Demmel, Applied Numerical Linear Algebra, SIAM 1997, selled at Cremona. List of Errata for the Textbook
    2. PETSc libraries which are a suite of data structures and routines for the scalable (parallel) solution of scientific applications; user manual
    Computer labs
    Wednesdays 13-15 (except the first week) in computer room MVF24 (Mathematical Sciences in Physics building).
    Fridays 13-15 in computer room MVF24 (exept the first week).
    Computer labs and Matlab/PETSc excercises will be included in the assignments below. Matlab programs which will be used in computer exercises:
  • polyplot.m
  • eigscat.m
  • qrplt.m
  • Templates for computer ex. 2:
  • Template for computing of discretized Laplacian
  • Template for the main program in PETSC for LU decomposition
  • Example of Makefile to be able compile PETSc program at Chalmers
  • Template for petsc function which removes zeros from the original matrix. We can work then with resulting matrix without zeros in the same way as with original matrix.
  • Example of the program in Matlab to present contour plot of the eigenvectors for the case of Poisson equation.

  • Reference literature:
    Course outline and requirements
    The following sections in the textbook will be considered in the book. Chapters 6 and 7 are saved for the another course.
    Chapter 1
    mainly repetition and brief revision on basic linear algebra.
    Chapter 2
    1-6, 7 except 2.7.4 and 2.7.5
    Chapter 3
    Chapter 4
    Chapter 5
    The following questions in the textbook are recommended: To each chapter belong an optional homework assignment and a computer exercise. The homework assignments are similar to the questions in the textbook and such you could expect at the examination. In the computer exercises you will be trained in using different algorithms in numerical linear algebra using MATLAB or PETSc libraries. Either you will use already existing MATLAB and PETSC programs or write your own small MATLAB or PETSc codes. The homework assignments give bonus credit points for the examination. Since the occasions reserved for the computer exercises are without supervision you may put questions on these exercises to me at the lectures. Passed computer exercises will be graded with grades 3, 4, or 5, see examination below.

    You may work in a group of 2 persons but hand in only one report for the group.

    Wednesdays 13-15 (except the first week) in computer room MVF24 (Mathematical Sciences at Physics building) Fridays 13-15 in computer room MVF24 (exept the first week when it is in room MVF25). Hand in a short report of your work before the final exam.


    Written examination
  • Final exam is compulsory, written.
  • The theory questions will be choosen from the following list
  • List of questions
  • You should be able to state and explain all definitions and theorems given in the course and also apply them in problem solving.
  • Grades are set according to the table below.
  • Grades Chalmers Points Grades GU Points
    - <15 -
    3 15-20 G 15-27
    4 21-27 VG >27
    5 >27
    Bring ID and receipt for your student union fee (this is requirement only for Chalmers students. GU students can come on the exam without receipt).

    Solutions to the exam will be published at the following link (will be added). You will be notified the result of your exam by email from LADOK (This is done automatically as soon as the exams have been marked an the results are registered.)
    The exams will then be kept at the students office in the Mathematical Sciences building.
    Check that the number of points and your grade given on the exam and registered in LADOK coincide.
    Complaints of the marking should be written and handed in at the office. There is a form you can use, ask the person in the office.).

    The following link will tell you all about the examination room rules at Chalmers: Examination room instructions

    Examination procedures
    In Chalmers Student Portal you can read about when exams are given and what rules apply on exams at Chalmers.
    At the link Schedule you can find when exams are given for courses at University of Gothenburg.
    At the exam, you should be able to show valid identification.
    Before the exam, it is important that you report that you want to take the examination. If you study at Chalmers, you will do this by the Chalmers Student Portal, and if you study at University of Gothenburg, so sign up via GU's Student Portal.

    You can see your results in Ladok by logging on to the Student portal.

    At the annual examination:
    When it is practical a separate review is arranged. The date of the review will be announced here on the course website. Anyone who can not participate in the review may thereafter retrieve and review their exam on Mathematical sciences study expedition, Monday through Friday, from 9:00 to 13:00. Check that you have the right grades and score. Any complaints about the marking must be submitted in writing at the office, where there is a form to fill out.

    At re-examination:
    Exams are reviewed and picked up at the Mathematical sciences study expedition, Monday through Friday, from 9:00 to 13:00. Any complaints about the marking must be submitted in writing at the office, where there is a form to fill out.
    Old exams
    Old exams are given here:
  • Old exams
  • Old exams 2012/2013
  • Old exams 2013/2014