Numerical Linear Algebra


The course will start with a pre-study week from October 6 - 10, 2014. The following exercises will hopefully give you a smooth introduction into the topic. You can solve these problems using the lecture notes and other textbooks you find helpful.

Instructions and material for pre-study week

Instructions PDF
Lecture notes PDF
Pre-study No 1 PDF
Pre-study No 2 PDF
Pre-study No 3 PDF
Pre-study No 4 PDF
Pre-study No 5 PDF

How to send in answers

Please write the answers to the theoretical questions and send them as a pdf, it does not have to be typed, it could also be handwritten and you can send me a photo. For the other exercises send in your solutions as .m files.


A lecture week at KTH will follow from October 13 - 17, 2014. The lectures will take place at the main building of KTH (Lindstedtsvägen 3 and 5) in the following rooms:

Monday October 13, room 1537, floor 5, PDF

Tuesday October 14, room 4523, floor 5, PDF

Wedesday October 15, room 4523, floor 5, PDF

Thursday October 16, room 4523, floor 5, PDF

Friday October 17, room 4523, floor 5
Important: Bring your own laptop computers for the lecture week at KTH!
Updated lecture notes PDF

Preliminary schedule

Monday 9 - 11: Introduction, discussion of prestudy results
Monday 11 - 13: Condition and stability, direct methods
Monday 13 - 14: Lunch break
Monday 14 - 16: Programming
Monday 16 - 18: Discussion of programming results

Tuesday 9 - 13: Iterative methods
Tuesday 13 - 14: Lunch break
Tuesday 14 - 16: Programming
Tuesday 16 - 18: Discussion of programming results

Wednesday 9 - 13: Methods for eigenvalue problems
Wednesday 13 - 14: Lunch break
Wednesday 14 - 16: Programming
Wednesday 16 - 18: Discussion of programming results

Thursday 9 - 13: Methods for nonlinear problems
Thursday 13 - 14: Lunch break
Thursday 14 - 16: Programming
Thursday 16 - 18: Discussion of programming results

Friday 9 - 11: Multigrid methods
Friday 11 - 13: Conclusion


For a project, use a method of your choice to generate a matrix. This can be from a discretization of a PDE or from a problem you work within your Ph.D project, etc. The only requirement it should meet is that the size is changeble, e.g. by choosing a different discretization parameter for your PDE.
  • In each project, the condition number of your matrix should be estimated by the computation of the smallest and largest eigenvalue.
  • Some more than just the smallest and largest eigenvalue should be computed.
  • Solve linear systems of different sizes, such that you reach a point where Matlab becomes unusable.
  • Examine the stability of your algorithms by changing the input or paramters slightly.