Algorithms of Scientific Computing - Summer 13

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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

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 IPyNb python 15.5.2013 IPyNb solution
5 Norms of Functions Worksheet 5 IPyNb python 22.5.2013 solution5.pdf IPyNb solution
6 Multi-dimensional Quadrature Worksheet 6, exercise6.ods 29.5.2013 solution6.pdf
7 Hierarchization in Higher Dimensions, Combination Technique Worksheet 7 IPyNb python 5.6.2013 solution7.pdf IPyNb solution
8 Adaptive Sparse Grids, Orthogonality Worksheet 8 12.6.2013


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).

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

Wavelets

Space-filling Curves:

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