General information

Numerical Linear Algebra ENM-TMA265 and GU-MMA600 7.5 credit points

  • All examination works written at 23.10.2012 are verified and You can get information about Your grades at expedition. Ask personal at expedition about information in LADOK.
  • All examination works written at 17.01.2013 are verified and You can get information about Your grades at expedition. Ask personal at expedition about information in LADOK.
  • Contents:

    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 solving linear systems of equations we present Gaussian elimination with different pivoting strategies and blocking algorithms for higher performance using BLAS (basic linear algebra subroutines).
    • For least-squares problems we study QR-factorisation and singular value decomposition.
    • The methods for eigenvalue problems are based on transformation techniques for symmetric and non-symmetric matrices.
    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:

    • use numerical linear algebra as building bricks in computation.
    • make a linear algebra model of problems from the physical reality.
    • derive and use the numerical techniques needed for a professional solution of a given linear algebra problem.
    • use computer algorithms, programs and software packages to compute solutions to current problems.
    • critically analyze and give advice regarding different choices of models, algorithms, and software with respect to efficiency and reliability.
    • critically analyze the accuracy of the obtained numerical result and to present it in a visualized way.
    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 at 23.10.2012: 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 at 23.10 will be 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. At the latest lecture we have decided make re-examination at 17.01.2013 at 8.30. Please, follow this site to get exact information closer to the day of re-examination. Aboit re-examination at 17.01.2013: this date for re-examination is already in Chalmers studieportal. This means that Chalmers students can already register for this 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
    23.10.2012 8.30-12.30 Maskinhuset Examination
    With the 2 exceptions: 11.10.2012 and 18.10.2012: in MVF32.
    Link to the system ping pong:
  • Ping Pong
  • Teachers
    Course coordinator: Larisa Beilina,

    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

  • 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, with a maximum score of 27 points.
  • 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 >28
    5 >28

    The exam takes place at 23.10, Maskinhuset at Chalmers:

  • Maskinhuset

  • 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 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. You do this at Chalmers Student Portal.

    Notice of result is obtained only by email via Ladok. (Not verbally at study expedition.) This is done automatically when the results are registered. Check that you have the right grades and score.

    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. 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.

    Answers to exam questions are given here:
  • Examination 1 (23.10.2012)
  • Examination 2 (17.01.2013)

  • Old exams
    Old exams are given here:
  • Old exams