J.M. Melenk
Mondays 9:00-10:30, SEM 101C (4. Stock, gruener Turm),
Thursdays 15:00-17:00, SEM 101C
Class notes
The course will be based in part on the book by Y. Saad (Iterative methods for large sparse
systems). The first edition of this book (now out of print, but the second edition is
in print!) is available on the web
here
class notes are handed out as we go along:
- part 1: introduction, spectral radius, the problem of fill-in
- part 2: Cholesky factorization, simple linear iterations
- part 3: Jacobi, Gauss-Seidel, Young's theorem, Chebyshev acceleration
- part 4: Gradient methods
- part 5: GMRES and CG
- part 6: GiCG, convergence properties of CG and PCG
- part 7: general preconditioning techniques
- part 8: Introduction to multigrid: the two-grid method
- part 9: multigrid and full multigrid
Übungsblätter:
Matrices to play with
To download these files right click on the link and choose 'Save target as'. Select
the directory you wish to download the file to and change the 'Save as type' box to 'All files'
otherwise '.txt' wil be tagged onto the filename.
The following matrices have been downloaded from the
Matrix Market. The matrices are stored in the
Matrix Market file format
which can be read using the mmread
M-file. This file and the matrix data needs to be in the same directory (or the path changed
accordingly) as your script/file.
To read in a matrix to the variable A simply include
A=mmread('matrix_name.mtx')
in your script/function. Note A will be defined to be sparse - you don't need to
do anything else
- Symmetric Positive Definite Matrices:
- Non-symmetric Matrices:
Other Useful Material
Public Domain Software:
many Fortran und C packages for solving problems of numerical linear algebra, quadrature,
and ODEs are public domain and can be retrieved from
NetLib.
Many algorithms (and their C/Fortran implementation) are described in the book
Numerical Recipes in C
by
Press, Teukolsky, Vetterling, Flannery.
This book exists also on-line