Advanced numerical methods for science and engineering - DN3250
News
This course is completed
2012-06-07: Homework set 4 is available
2012-05-31: Homework set 4 (temporary version) is available
2012-05-15: Homework set 3 is available
2012-05-15: The previously postponed lecture will take place on 28/4
2012-05-04: The lecture on 2012-05-10 has, as we have discussed, been moved one hour forward in time
2012-04-27: The lecture originally planned for 30 April will be postponed, since it is a "klämdag" where lectures normally do not take place
2012-04-11: Homework set 2 is available.
2012-03-23: The dates, times and location for the lectures have been fixed. See below.
2012-03-14: The date and location of the first lecture has changed to Thursday 22/3.
Audience
The course is intended for the PhD students
in the PhD program KCSE.
General course description
This course aims to provide an overview of the modern techniques used in the solution of some of the most common numerical linear algebra problems arising in science and engineering, with special focus on the two topics
large linear systems of equations, and
large eigenvalue problems.
After the course, you will be able to approach these two problems with the following
skills:
Given a matrix/problem with a particular structure you will be able to identify
properties important for the choice of algorithm.
Given the structure of a matrix select an appropriate algorithm from the set of
common algorithms.
You should be able to use the selected algorithm by writing a C- or Fortran-program which links it with modern software packages.
In case of failure of algorithm, you should be able to analyze
the output of the algorithm and identify the source of the
error and propose one of the typical modifications.
The course is offered to all graduate students at KTH. Basic
knowledge in numerical
analysis (the courses DN1240 or DN1212 or equivalent) is a prerequisite.
We assume
that the student has a basic knowledge of programming in one of the languages
C or Fortran.
Preliminary schedule
Week When Where Subject (preliminary)
12 Thu 22/3 13-15 1537 Introduction
13 Wed 28/3 15-17 4523 Linear systems
13 Fri 30/3 15-17 1537 Linear systems
14 Mon 2/4 13-15 4523 Linear systems
14 Wed 4/4 13-15 4523 Linear systems
15 Thu 12/4 13-15 1537 Linear systems
16 Thu 19/4 13-15 1537 Linear systems + Intro eigenvalue problems
17 No lectures
(18 Mon 30/4 13-15 1537 Lecture postponed )
18 Fri 4/5 13-15 1537 Eigenvalue problems
19 Tue 8/5 15-17 4523 Eigenvalue problems
19 Thu 10/5 16-18 1537 Eigenvalue problems, note new time
20 Fri 18/5 13-15 1537 Eigenvalue problems
21 No Lectures
22 Mon 28/4 16-18 1537 Eigenvalue problems (prev. postponed)
22 Fri 1/6 15-17 1537 Eigenvalue problems
23 Tue 5/6 10-12 4523 Eigenvalue problems
The seminar rooms 1537 and 4523 are at the department of numerical analysis, Lindstedtsvägen 3, 5th floor,
Literature
Part 4-5 in [TB] Trefethen, Bau, Numerical linear algebra, ISBN:0-89871-361-7. This book is available online to all KTH students via KTHB. Here is a direct link.
The article H. A. van der Vorst, Bi-CGSTAB: A fast smoothly converging variant of Bi-CG for the solution of nonsymmetric linear systems. SIAM J. Sci. Stat. Comput., 1992, 13(2):630-644.
You can download this paper if you are at KTH.
Parts of the article D. Sorensen, Implicit application of polynomial filters in a k-step Arnoldi method,
SIAM J. Matrix Anal. Appl. 1992, 1:357-385.
You can download this paper if you are at KTH.
The article G. L. G. Sleijpen, H. A. Van der Vorst, A Jacobi-Davidson iteration method for
linear eigenvalue problems, SIAM Review, 2000, 42(2), 267-293, You can download this paper if you are at KTH.
Parts from the article P.-A. Absil, R. Mahony, R. Sepulchre, P. Van Dooren, A Grassmann-Rayleigh quotient iteration for computing invariant subspaces, SIAM Review, 44(1), pp. 57-73, 2002. You can download this paper if you are at KTH.
Manuals of the software packages
Hand-outs covering specific matrix structures and algorithms
Exercise material
Homework set 1: Linear systems (LU decomposition, Cholesky decomposition, Symmetry, sparsity, Rank-one update structures). You will need back_fw_subs.m.
Homework set 2: Linear systems (CG (matlab), matrix-vector product, BiCGstab (fortran)). You will need
to use hw2_runbcg.f
Homework set 3: Eigenvalue problems (QR method, inverse iteration)