- 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.

- large linear systems of equations, and
- large eigenvalue problems.

- 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.

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 problemsThe seminar rooms 1537 and 4523 are at the department of numerical analysis, Lindstedtsvägen 3, 5th floor,

- 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

- 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)
- Homework set 4: Eigenvalue problems (ARPACK (fortran/C), Jacobi-Davidson (matlab)). You will need arnupd.m, arnoldi_sorensen.m and arnoldi_standard.m.