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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 repeat exam: Friday, Oct 18, 2013, 16:30-18:15 (Interimshörsaal 2), 1 handwritten DinA4 page (both sides) is the only allowed aid
repeat exam review: see below under News
Semesterwochenstunden / ECTS Credits
6 SWS (4V + 2Ü) / 8 Credits
TUMonline
Algorithms of Scientific Computing



Contents

News & Announcements

  • Instead of a last tutorial, there will be a Q&A session with both tutors on Wednesday, July 17, 10-11.30am
  • The time and place of the exam are announced above.
  • On July 10/11, lecture and tutorial will be switched:
    • July 10, 10-12: lecture in MI 02.07.023
    • July 11, 10-12: tutorial in MI 01.10.011
  • 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.
  • repeat exam review: date (Mo October 28, 2013), time (13.00-14.00), room (02.07.023)

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 py/ipynb 15.5.2013 IPyNb solution
5 Norms of Functions Worksheet 5 py/ipynb 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 py/ipynb 5.6.2013 solution7.pdf IPyNb solution
8 Adaptive Sparse Grids, Orthogonality Worksheet 8 12.6.2013 solution8.pdf
9 Scaling Functions, The Haar Wavelet Family Worksheet 9 py/ipynb 20.6.2013 IPyNb solution
10 Space-filling Curves, Warm up Worksheet 10 26.6.2013 ---
11 Grammars for Space-filling Curves Worksheet 11 py(template) 3.7.2013 solution 11 py(solution)
12 Arithmetization of Space-filling Curves Worksheet 12 py(template) 10.7.2013 solution 12 py(solution)

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 repeat exam, duration: 90 min
  • time, date, room: Fri Oct 18, 2013, 16.30-18.15 (Interim 2 - in the black building in front of FMI)
    • note that the exam will start precisely on 16.30; please be in the exam room by 16.15, at the latest!
  • helping material:
    • you may use one hand-written sheet of paper (size A4, front and back may be used)
    • no other helping material of any kind is allowed
  • please make sure that you register in TUMonline
  • exam review: t.b.a. (probably around 1 week after the repeat exam)

Literature and Additional Material

Fast Fourier Transform:

The lecture is oriented on:

Hierarchical Methods and Sparse Grids

Wavelets

Space-filling Curves: