Difference between revisions of "Algorithms for Scientific Computing - Summer 17"

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| 8 || Multi-dimensional Quadrature || [http://www5.in.tum.de/lehre/vorlesungen/asc/ss17/blatt8/ws8.pdf Worksheet 8] [http://www5.in.tum.de/lehre/vorlesungen/asc/ss17/blatt8/arch2d_exercise.ods Worksheet 8 template] || Jun. 28 ||  
 
| 8 || Multi-dimensional Quadrature || [http://www5.in.tum.de/lehre/vorlesungen/asc/ss17/blatt8/ws8.pdf Worksheet 8] [http://www5.in.tum.de/lehre/vorlesungen/asc/ss17/blatt8/arch2d_exercise.ods Worksheet 8 template] || Jun. 28 ||  
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[http://www5.in.tum.de/lehre/vorlesungen/asc/ss17/blatt8/arch2d_solution.ods Ws8 solution]
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| 9 || Multi-dimensional hierarchization and adaptive sparse grids || [http://www5.in.tum.de/lehre/vorlesungen/asc/ss17/blatt9/ws9.pdf Worksheet 9] [http://www5.in.tum.de/lehre/vorlesungen/asc/ss17/blatt9/ws9_code_template.zip Worksheet 9 code template] || Jul. 05 ||
 
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[http://www5.in.tum.de/lehre/vorlesungen/asc/ss16/blatt8/arch2d_solution.ods Ws8 solution]
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[http://www5.in.tum.de/lehre/vorlesungen/asc/ss17/blatt9/ws9_code_solution.zip Ws9 code solution] [http://www5.in.tum.de/lehre/vorlesungen/asc/ss17/blatt9/ws9_ex2_solution.pdf Ws9 Ex2 solution]
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| 9 || Multi-dimensional hierarchization and adaptive sparse grids || [http://www5.in.tum.de/lehre/vorlesungen/asc/ss16/blatt9/ws9.pdf Worksheet 9] [http://www5.in.tum.de/lehre/vorlesungen/asc/ss16/blatt9/ws9_code_template.zip Worksheet 9 code template] || Jun. 15 ||[http://www5.in.tum.de/lehre/vorlesungen/asc/ss16/blatt9/ws9_code_solution.zip Ws9 code solution] [http://www5.in.tum.de/lehre/vorlesungen/asc/ss16/blatt9/ws9_ex2_solution.pdf Ws9 Ex2 solution]
 
 
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| 10 || Grammars for space-filling curves || [http://www5.in.tum.de/lehre/vorlesungen/asc/ss16/blatt10/ws10.pdf Worksheet 10] [http://www5.in.tum.de/lehre/vorlesungen/asc/ss16/blatt10/ws10_code_template.zip Worksheet 10 code template] [http://www5.in.tum.de/lehre/vorlesungen/asc/ss16/blatt10/ws10_template.ipynb Notebook template] || Jun. 22 || [http://www5.in.tum.de/lehre/vorlesungen/asc/ss16/blatt10/ws10_solution.pdf Ws10 solution ] [http://www5.in.tum.de/lehre/vorlesungen/asc/ss16/blatt10/ws10_code_solution.zip Ws10 solution code] [http://www5.in.tum.de/lehre/vorlesungen/asc/ss16/blatt10/ws10_solution.ipynb Ws10 solution Notebook]
 
| 10 || Grammars for space-filling curves || [http://www5.in.tum.de/lehre/vorlesungen/asc/ss16/blatt10/ws10.pdf Worksheet 10] [http://www5.in.tum.de/lehre/vorlesungen/asc/ss16/blatt10/ws10_code_template.zip Worksheet 10 code template] [http://www5.in.tum.de/lehre/vorlesungen/asc/ss16/blatt10/ws10_template.ipynb Notebook template] || Jun. 22 || [http://www5.in.tum.de/lehre/vorlesungen/asc/ss16/blatt10/ws10_solution.pdf Ws10 solution ] [http://www5.in.tum.de/lehre/vorlesungen/asc/ss16/blatt10/ws10_code_solution.zip Ws10 solution code] [http://www5.in.tum.de/lehre/vorlesungen/asc/ss16/blatt10/ws10_solution.ipynb Ws10 solution Notebook]

Revision as of 09:30, 28 June 2017

Term
Summer 2017
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 24)
Tutorial: Wed 10:15-11:45, MI 00.13.09A
Audience
see module description (IN2001) in TUMonline
Tutorials
Emily Mo-Hellenbrand, M.Sc., Jean-Matthieu Gallard, 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=950290914



News & Announcements

  • Worksheet 7 solution is updated (mistake in ex4 corrected). Please re-check the solution!
  • please re-check the solution of exercise 1 on worksheet 4; this has been corrected!
  • as an exception, the lecture on Fri, May 19, will start at 10.30 (until 12.00)

What's ASC about?

Many applications in computer science require methods of (numerical) mathematics - especially in science and engineering, of course, but also 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. Similar, numerical methods for approximation have become essential techniques for high-dimensional classification problems in data science. Essentially, these methods come down to the question of how to represent and process information or data as (multi-dimensional) continuous functions. "Algorithms for Scientific Computing" thus provides an algorithmically oriented introduction to the foundations of such mathematical methods.

Topics include:

  • The fast Fourier transformation (FFT) and some of its variants:
    • FCT (Fast Cosine Transform), real FFT, Application for compression of video and audio data
  • Hierarchical and recursive methods in scientific computing
    • From Archimedes' quadrature to the hierarchical basis
    • Classification problems
    • From the hierarchical basis to wavelets
  • High-demonsional problems
    • Sparse grids and the sparse-grid combination technique
  • Octrees and Space filling curves (SFCs):
    • Tree-structured (hierarchical) adaptivity
    • Construction and properies of SFCs
    • Application for parallelization and to linearize multidimensional data spaces in data bases

Lecture Slides and Supplementary Materials

Lecture slides are published here successively. For future lectures, the respective slides from summer 2016 will be linked.

Fast Fourier Transform

Hierarchical Methods

Sparse Grids


Worksheets and Solutions

Number Topic Worksheet Tutorial Solution
1 Discrete Fourier Transform I Worksheet 1Python Introduction Apr. 26

Ws1 solution Ws1 solution Notebook

2 Discrete Fourier Transform II Worksheet 2 Worksheet 2 Notebook template May 3

Ws2 solution Ws2 solution Notebook Ws2 Ex2 solution code

- - - May 10 tutorial cancelled due to student assembly
3 Discrete Cosine Transform Worksheet 3 Worksheet 3 Notebook template Template Exercise 1 May 17

Ws3 solution Ws3 solution code

4 Discrete Fourier Transform III Worksheet 4 May 24

Ws4 solution

5 Numerical Quadrature 1D Worksheet 5 Worksheet 5 Notebook template May 31

Ws5 solution Notebook

6 Hierarchical Basis Worksheet 6 Jun. 07

Ws6 Ex1-2 solution Notebook Ws6 Ex3 solution

7-Part1 Function Approximation and Wavelet Ex1-3: Worksheet 7 Worksheet 7 Notebook template Jun. 14

Ws7 solution

7-Part2 Function Approximation and Wavelet Ex4-5: See above Jun. 21 See above
8 Multi-dimensional Quadrature Worksheet 8 Worksheet 8 template Jun. 28

Ws8 solution

9 Multi-dimensional hierarchization and adaptive sparse grids Worksheet 9 Worksheet 9 code template Jul. 05


Jupyter Notebook


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:

Hierarchical Methods and Sparse Grids

Wavelets

Space-filling Curves:

Background Material Concerning Scientific and High Performance Computing