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October 2017
Hej!
You are receiving this email because you are registered or partially registered in the course SF2524 Matrix computations for large-scale systems. The first lecture for SF2524 is on Tuesday, October 31.
I have two requests before the first lecture:
- We use canvas in this course. In order to follow the course and get complete access to the canvas pages, you need to register for the course. This is done by you, and can usually be done directly through the web (via your personal top gray bar on the top of this page).
- I would like you to have a look at the file background.pdf and do the quiz background on CANVAS preferably before the first lecture. The topics in background concern things which students in some universities have seen before, and some of you have not. The quiz is for your training only. It can be done as many times as you like and will not be counted to any form of grade.
Future messages will only be sent through the CANVAS system and not posted on KTH social.
On behalf of the teachers (me and Parikshit Upadhyaya), I wish you very welcome to the course,
Elias
January 2017
Hej again, I have not received many course evaluations. Please fill it out here
In particular, I am very interested in hearing your comments about the wiki training area, since it was the first time we used it. The result of the course evaluation will be used to further develop the course and it will be discussed by the board of the master programme(s).
Good luck with further studies!
December 2016
Hej,
Some final messages:
1. Please fill out a course evaluation. This is important for the teachers such that we know how to improve the course. This year, we had quite a few students who dropped out after the first lecture. If you decided to drop out of the course you are still welcome to fill out the evaluation and specify the reason.
Based on my view on the course, we intend to do the following changes for next year:
- More written self-contained material for Block 1 and at the end of Block 2
- Make wiki-questions not a strict requirement for all HW, but only for bonus.
- Integrate video material more into the course
2. The selected exercises have now been finalized and together with the Old exams, should be a solid basis as exam preparation. The selected exercises and together with solutions are now available as a single PDF-file. The other exercises on the wiki may also valuable in the preparation for the exam, although some problems lack solutions and not all solutions are complete. I have enjoyed teaching the course. I am in general quite happy with the level of understanding I have seen so far; also in comparison to the corresponding course at other universities. Let's hope we will see the same thing on the exam. Please study hard for the exam.
November 2016
Hej, the Lanczos method video is now online.
Note that the video is purposely playing fast. You will need to pause to understand it.
Elias
December 2015
Hej,
Homework 3 is now corrected and all master students who handed in homework 3 passed. I am still expecting a revision of homework 2 from 6 students.
The lectures of this course are almost over. I have enjoyed teaching this course. If you enjoyed learning this material, you are very welcome to write so in the course evaluation. More importantly, if you did not enjoy it and you think there are things to improve in this course, I very much appreciate such comments, such that the course improves next year:
We already have two improvements that we will implement next year:
- One more lecture on preconditioning
- Further written material on convergence of the QR-method
Elias
Teacher
Elias Jarlebring
edited
11 December 2015
Hej,
Homework 3 is now corrected and all master students who handed in homework 3 passed. I am still expecting a revision of homework 2 from 6 students.
The course is lectures of this course are almost over. I have enjoyed teaching this course. If you enjoyed learning this material, you are very welcome to write so in the course evaluation. More importantly, if you did not enjoy it and you think there are things to improve in this course, I very much appreciate such comments, such that the course improves next year:
We already have two improvements that we will implement next year:
* One more lecture on preconditioning
* Further written material on convergence of the QR-method
Elias
November 2015
Hej!
I hope the first homework is going well.
Some hints / clarifications for HW1 based on email questions:
problem 2: On some computers 10 minutes of execution time is difficult to test due to limitations in RAM. It is not so important that you achieve 10 minutes in those situations, if you can show that you interpret the result correctly. The commands "rand('seed',0); A=gallery(’wathen’,nn,nn);" generate a sparse matrix of size nn^2 x nn^2. For the purpose of learning what you are expected to understand in the exercise, it is not so important to understand exactly how the matrix is generated. (It is matrix with sparsity structure like a particular finite-element discretizations. The non-zero elements are generated randomly, so we need to do reset the random seed in order get the same results every time we run the command.")
problem 4c. The relationship between shift-and-invert Arnoldi and the standard Arnoldi method is completely analogous to the relationship between inverse iteration and the power method. So, instead of Arnoldi's method for \(B\) you need to do Arnoldi's method for the matrix \((B-\sigma I)^{-1}\) without explicitly computing the inverse, but only solve linear systems of equations. You will need to modify arnoldi.m. Don't forget to reverse the eigenvalue transformation. We will show an example of shift-and-inverse on the next lecture (tuesday).
Elias
Teacher
Elias Jarlebring
edited
8 November 2015
Hej!
I hope the first homework is going well.
Here is some more hint for HW1 problem 4c. The relationship between shift-and-invert Arnoldi and the standard Arnoldi method is completely analogous to the relationship between inverse iteration and the power method. So, instead of Arnoldi's method for tex:\displaystyle B you need to do Arnoldi's method for the matrix tex:\displaystyle (AB-\sigma I)^{-1} without explicitly computing the inverse, but only solve linear systems of equations. You will need to modify arnoldi.m. Don't forget to reverse the eigenvalue transformation. We will show an example of shift-and-inverse on the next lecture (tuesday).
Elias
Teacher
Elias Jarlebring
edited
8 November 2015
Hej!
I hope the first homework is going well.
Here is some more hint for HW1Some hints / clarifications for HW1:¶
problem 2: The commands "rand('seed',0); A=gallery(’wathen’,nn,nn);" generate a sparse matrix of size nn^2 x nn^2. For the purpose of learning what you are expected to understand in the exercise, it is not so important to understand how the matrix is generated. (It is matrix with sparsity structure like a particular finite-element discretizations. The non-zero elements are generated randomly, so we need to do reset the random seed in order get the same results every time we run the command.")¶
problem 4c. The relationship between shift-and-invert Arnoldi and the standard Arnoldi method is completely analogous to the relationship between inverse iteration and the power method. So, instead of Arnoldi's method for tex:\displaystyle B you need to do Arnoldi's method for the matrix tex:\displaystyle (B-\sigma I)^{-1} without explicitly computing the inverse, but only solve linear systems of equations. You will need to modify arnoldi.m. Don't forget to reverse the eigenvalue transformation. We will show an example of shift-and-inverse on the next lecture (tuesday).
Elias
Teacher
Elias Jarlebring
edited
8 November 2015
Hej!
I hope the first homework is going well.
Some hints / clarifications for HW1:
problem 2: On some computers 10 minutes of execution time is difficult to test due to limitations in RAM. It is not so important that you achieve 10 minutes in those situations, if you can show that you interpret the result correctly. The commands "rand('seed',0); A=gallery(’wathen’,nn,nn);" generate a sparse matrix of size nn^2 x nn^2. For the purpose of learning what you are expected to understand in the exercise, it is not so important to understand exactly how the matrix is generated. (It is matrix with sparsity structure like a particular finite-element discretizations. The non-zero elements are generated randomly, so we need to do reset the random seed in order get the same results every time we run the command.")
problem 4c. The relationship between shift-and-invert Arnoldi and the standard Arnoldi method is completely analogous to the relationship between inverse iteration and the power method. So, instead of Arnoldi's method for tex:\displaystyle B you need to do Arnoldi's method for the matrix tex:\displaystyle (B-\sigma I)^{-1} without explicitly computing the inverse, but only solve linear systems of equations. You will need to modify arnoldi.m. Don't forget to reverse the eigenvalue transformation. We will show an example of shift-and-inverse on the next lecture (tuesday).
Elias
Teacher
Elias Jarlebring
edited
8 November 2015
Hej!
I hope the first homework is going well.
Some hints / clarifications for HW1 based on email questions:
problem 2: On some computers 10 minutes of execution time is difficult to test due to limitations in RAM. It is not so important that you achieve 10 minutes in those situations, if you can show that you interpret the result correctly. The commands "rand('seed',0); A=gallery(’wathen’,nn,nn);" generate a sparse matrix of size nn^2 x nn^2. For the purpose of learning what you are expected to understand in the exercise, it is not so important to understand exactly how the matrix is generated. (It is matrix with sparsity structure like a particular finite-element discretizations. The non-zero elements are generated randomly, so we need to do reset the random seed in order get the same results every time we run the command.")
problem 4c. The relationship between shift-and-invert Arnoldi and the standard Arnoldi method is completely analogous to the relationship between inverse iteration and the power method. So, instead of Arnoldi's method for tex:\displaystyle B you need to do Arnoldi's method for the matrix tex:\displaystyle (B-\sigma I)^{-1} without explicitly computing the inverse, but only solve linear systems of equations. You will need to modify arnoldi.m. Don't forget to reverse the eigenvalue transformation. We will show an example of shift-and-inverse on the next lecture (tuesday).
Elias
March 2015
Hej, The re-exam takes place on Tuesday April 7, 08:00-12:00 (four hours) in lecture hall V01. Please disregard other web pages which have previously stated a different location. Good luck! /Elias
February 2015
Hej,
The exams are now corrected and reported into the system. The results should appear in rapp (rapp.csc.kth.se) and on "Mina sidor" within a couple of working days. I am overall happy with results. The exam and solution can be found here.
We always want to improve courses at KTH. Your feedback is very important for us in order to do so. I would appreciate very much if you could fill out a course evaluation:
Thanks!
December 2014
There will be an extra lecture on Friday Dec. 19 at 13:15-15:00 in the seminar room 3733 of the KTH Mathematics building. The seminar room is located on the top floor of Lindstedtsvägen 25. This lecture is not visible in the official "schedule".
Teacher
Elias Jarlebring
edited
17 December 2014
There will be an extra lecture on Friday Dec. 19 at 13:15-15:00 in the seminar room 3733 of the KTH Mathematics building. The seminar room is located on the top floor of Lindstedtsvägen 25. This lecture is not visible in the official "schedule".
Teacher
Elias Jarlebring
changed the permissions
9 December 2014
Kan därmed läsas av alla och ändras av elias jarlebring (eliasj@kth.se).
November 2014
Teacher
Elias Jarlebring
edited
25 November 2014
There is a now a PDF-file with the pseudo-code for GMRES on the course web page. The pseudocode gives some more detail than TB.
The delivery of the course book "Numerical linear algebra, Trefethen & Bau" to Kårbokhandeln was delayed, but they have now (today) arrived.
October 2014
Hej registered participants of the course SF2524,
Welcome to this course which starts on tuesday next week (Nov 4, 2014). Note that the time of the first lecture was rescheduled some time ago. In this course we will use "KTH social" for essentially all online information. The main page has been recently been updated, and will be updated throughout the course.
The main literature in this course will be the book of Trefethen and Bau. I recommend trying to get hold of this book very soon. It should be available in "Kårbokhandeln".
The participants of a PhD-level course (numerical linear algebra) are also expected to attend the lectures of this course, so do not be startled by the older in the audience in the first lecture.
Welcome!
The lecturer, Elias
