Algorithms for Scientific Computing - Summer 16
- Term
- Summer 2016
- Lecturer
- Univ.-Prof. Dr. Michael Bader
- Time and Place
- Lecture: Mon 8:30-10:00, Fri 10:15-11:45, MI Hörsaal 2 (1st lecture: Mon, Apr 11)
- Tutorial: Wed 10:15-11:45, MI 00.09.013A
- Audience
- see module description (IN2001) in TUMonline
- Tutorials
- Emily Mo-Hellenbrand, M.Sc., Angelika Schwarz, M.Sc.
- Exam
- written exam at the end of the semester
- Semesterwochenstunden / ECTS Credits
- 6 SWS (4V + 2Ü) / 8 Credits
- TUMonline
- https://campus.tum.de/tumonline/wblv.wbShowLvDetail?pStpSpNr=950238554
News & Announcements
- Sheet 3 Exercise 2 has been updated. The input dataset is now explicitly real-valued.
- Due to the student assembly, there is no tutorial on April 27.
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
Lecture Slides and Supplementary Materials
Lecture slides will be published here as soon as they become available. For future lectures, the respective slides from summer 2015 will be linked.
- Introduction - Apr 11
Fast Fourier Transform
- Discrete Fourier Transform (DFT) - Apr 15
- Fast Fourier Transform (FFT) - Apr 15, 18
- 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, 25
- additional info: paper Paul N. Swarztrauber - Symmetric FFTs (access via LRZ proxy necessary, see also the paper on the AMS website)
- Quarter-Wave-Fourier Transform and Discrete Cosine Transform - Apr 25, 29
- matlab central: jpeg compression
- an embarrassingly simple simple JPEG-simulator (Java program)
- Discrete Sine Transform - May 2
- Fast Poisson Solvers - pres. May 6
Worksheets and Solutions
| Number | Topic | Worksheet | Tutorial | Solution |
|---|---|---|---|---|
| 1 | Discrete Fourier Transform I | Worksheet 1Python Introduction | Apr. 13 | Worksheet 1 solution IPyNb Worksheet 1 solution |
| 2 | Discrete Fourier Transform II | Worksheet 2 IPyNb Worksheet 2 template | Apr. 20 | Worksheet 2 solution IPyNb Worksheet 2 solution Code Exercise 2 solution |
| - | - | - | Apr. 27 | tutorial cancelled due to student assembly |
| 3 | Discrete Cosine Transform | Worksheet 3 IPyNb Worksheet 3 template Template Exercise 1 | May 6 | Worksheet 3 solution Code Worksheet 3 solution |
| 4 | Discrete Sine Transform | Worksheet 4 | May 11 | not yet available |
IPython Notebook
- If you want to use a local installation of IPython Notebook on your laptop or home computer, just refer to the IPython Notebook website on how to install IPython Notebook on Linux, Windows or MAC platforms
- If you install IPython Notebook for Windows, it might happen that starting it from the "Start" menue will open an IPython server website, but that you cannot create or import any new Python notebooks. In that case, try to start IPython Notebook from the command line via "ipython notebook --notebook-dir=.\" (from the directory where you want to store the Python notebooks); you can also create a batch file for this (download example, place it in the desired directory).
Literature and Additional Material
Books that are labeled as "available as e-book" can be accessed as e-book via the TUM library - see the ebooks website of the library for details on how to access the books.
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 (available as e-book)
- 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 (available as e-book)
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 (available as e-book).
- Collection of Wavelet tutorials (maintained by E. Aboufadel and S. Schlicker)
- 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, also in the TUM library) - Hans Sagan: Space-Filling Curves, Springer-Verlag, 1994
Background Material Concerning Scientific and High Performance Computing
- From the lecture HPC - Algorithms and Applications: Fundamentals - Parallel Architectures, Models, and Languages (esp.: Roofline Model, Cache Models, etc.)
- read the related paper: Roofline: An Insightful Visual Performance Model for Floating-Point Programs and Multicore Architectures (technical report by Williams et al.; published in Communications of the ACM 52 (4), 2009, p.65-76)