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

Term
Summer 2017
Lecturer
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
Mon, Aug 7, 10.30 in lecture hall MI HS 1 (F.L. Bauer Hörsaal)
Semesterwochenstunden / ECTS Credits
6 SWS (4V + 2Ü) / 8 Credits
TUMonline
https://campus.tum.de/tumonline/wbLv.wbShowLVDetail?pStpSpNr=950290914

News & Announcements

• The supplement material of transforming the regularization formula into a linear system (Lecture July 10, slide 18) is uploaded.
• Worksheet 9 code template is updated (fixed compatibility issues with Python 3). Please re-download the template zip. NOTE: you need the files supplied in the template zip to run the Worksheet 9 code solution.
• 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)

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):
• 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.

Worksheets and Solutions

Number Topic Worksheet Tutorial Solution
1 Discrete Fourier Transform I Worksheet 1Python Introduction Apr. 26
2 Discrete Fourier Transform II Worksheet 2 Worksheet 2 Notebook template May 3
- - - May 10 tutorial cancelled due to student assembly
3 Discrete Cosine Transform Worksheet 3 Worksheet 3 Notebook template Template Exercise 1 May 17
4 Discrete Fourier Transform III Worksheet 4 May 24
5 Numerical Quadrature 1D Worksheet 5 Worksheet 5 Notebook template May 31
6 Hierarchical Basis Worksheet 6 Jun. 07
7-Part1 Function Approximation and Wavelet Ex1-3: Worksheet 7 Worksheet 7 Notebook template Jun. 14
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
9 Multi-dimensional hierarchization and adaptive sparse grids Worksheet 9 Worksheet 9 code template Jul. 05

Exam

• type: written exam, duration: 100 min
• time, date, room: Mon, Aug 7, 2017, 10.30-12.10 (MI HS 1, Friedrich L. Bauer Hörsaal)
• note that the exam will start precisely on 10.30; please be in the exam room by 10.15, 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
• extra session for questions: t.b.a.

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: