Algorithms of Scientific Computing - Summer 13
- Term
- Summer 13
- Lecturer
- Michael Bader
- Time and Place
- Mondays 8:30-10:00 (MI HS 3) and Thursdays 10-12, room MI 01.10.011, starting April 15
- Tutorial: Wednesdays 10:15-11:45, room MI 02.07.023
- Audience
- see TUMonline
- Tutorials
- Gerrit Buse, Denis Jarema
- Exam
- written exam
- Semesterwochenstunden / ECTS Credits
- 6 SWS (4V + 2Ü) / 8 Credits
- TUMonline
- Algorithms of Scientific Computing
News & Announcements
- The lecture on Thursday, May 2, will take place in seminar room MI 02.07.023, as the regular seminar room is occupied by another lecture.
What's ASC about?
Many applications in computer science require methods of (prevalently numerical) mathematics - especially in science and engineering, of course, but as well in surprisingly many areas that one might suspect to be directly at the heart of computer science:
Consider, for example, Fourier and wavelet transformations, which are indispensable in image processing and image compression. Space filling curves (which have been considered to be "topological monsters" and a useless theoretical bauble at the end of the 19th century) have become important methods used for parallelization and the implementation of data bases. Numerical methods for minimization and zero-setting are an essential foundation of Neural Networks in machine learning.
Essentially, these methods come down to the question of how to represent and process information or data as (multi-dimensional) continuous functions. Algorithms of Scientific Computing (former Algorithmen des Wissenschaftlichen Rechnens) provides a generally understandable and algorithmically oriented introduction into the foundations of such mathematical methods. Topics are:
- The fast Fourier transformation (FFT) and some of its variants:
- FCT (Fast Cosine Transform), real FFT, Application for compression of video and audio data
- Space filling curves (SFCs):
- Construction and properies of SFCs
- Application for parallelization and to linearize multidimensional data spaces in data bases
- Hierarchical and recursive methods in scientific computing
- From Archimede's quadrature to the hierarchical basis
- Cost vs. accuracy
- Sparse grids, wavelets, multi-grid methods
Material
Lecture slides and worksheets will be published here as soon as they become available.
Fast Fourier Transform
- Discrete Fourier Transform (DFT) - Apr 15,18
- Fast Fourier Transform (FFT) - Apr 18, 22
- Further Material: Website of FFTW (a fast library to compute the DFT); in particular, see the chapter on Implementing FFTs in Practice by the FFTW developers
- FFT on real data - Apr 22, 29
- additional info: paper Paul N. Swarztrauber - Symmetric FFTs (access via LRZ proxy necessary, or see the preprint on the NCAR website)
- Quarter-Wave-Fourier Transform and Discrete Cosine Transform - Apr 29, May 2,6
- matlab central: jpeg compression
- an embarrassingly simple simple JPEG-simulator (Java program)
- Discrete Sine Transform - May 6
- Fast Poisson Solvers - May 6 (started)
Hierarchical Methods
Space-Filling Curves
Worksheets and Solutions
| Number | Topic | Worksheet | Date | Solution |
|---|---|---|---|---|
| 1 | Discrete Fourier Transform I | Worksheet 1 Python Introduction | 17.4.2013 | solution pallas1 pallas2 |
| 2 | Discrete Fourier Transform II | Worksheet 2 | 25.4.2013 | solution |
| 3 | Discrete Cosine Transformation | Worksheet 3 | 8.5.2013 | solution |
| 4 | Numerical Quadrature for One-dimensional Functions | Worksheet 4 | 15.5.2013 |
Exam
- written exam
- time, date, room: to be announced
Literature and Additional Material
Fast Fourier Transform:
The lecture is oriented on:
- W.L. Briggs, Van Emden Henson: The DFT - An Owner's Manual for the Discrete Fourier Transform, SIAM, 1995
- Thomas Huckle, Stefan Schneider: Numerische Methoden - Eine Einführung für Informatiker, Naturwissenschaftler, Ingenieure und Mathematiker, Springer-Verlag, Berlin-Heidelberg, 2.Auflage 2006 (German only)
- Charles van Loan: Computational Frameworks for the Fast Fourier Transform, SIAM, 1992
Hierarchical Methods and Sparse Grids
- Skript of H.-J. Bungartz for the lecture "Rekursive Verfahren und hierarchische Datenstrukturen in der numerischen Analysis" (German only)
- General overview paper on Sparse Grids
- Chapter on Sparse Grids in this book
Wavelets
- E. Aboufadel, S. Schlicker: Discovering Wavelets, Whiley, New York, 1999.
- J.S. Walker: A Primer on Wavelets and their Scientific Applications, Second Edition, Chapman and Hall/CRC, 2008.
- J.S. Walker: Wavelet-based Image Compression (download as PDF)
Space-filling Curves:
- Michael Bader: Space-Filling Curves - An introduction with applications in scientific computing, Texts in Computational Science and Engineering 9, Springer-Verlag, 2012
( available as eBook) - Hans Sagan: Space-Filling Curves, Springer-Verlag, 1994