Low Rank Approximation: Difference between revisions
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The first lecture will be | The first lecture will be on Monday, 16.4.2018, 2pm (14:00) in room 02.08.020, M11. | ||
TUMOnline | The lecture dates have been fixed to 16.4., 23.4., 30.4., 14.5., 28.5., 4.6., 11.6., 18.6., | ||
25.6., 2.7. (Monday 2pm) | |||
See also TUMOnline at https://campus.tum.de/tumonline/wbLv.wbShowLVDetail?pStpSpNr=950377693&pSpracheNr=1 | |||
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= Lecture slides = | = Lecture slides = | ||
* Slides 1: Basic concepts and subspace iteration [http://www5.in.tum.de/lehre/vorlesungen/parnum/WS17/lecture_1.pdf lecture_1.pdf] | |||
* Slides 2: | |||
= Literature & external links = | = Literature & external links = | ||
Pointers to the literature can be found in the slides. | |||
<!-- * Eijkhout, Chow, van de Geijn: [http://www.lulu.com/product/paperback/introduction-to-high-performance-scientific-computing/14455750 Introduction to High Performance Scientific Computing] | <!-- * Eijkhout, Chow, van de Geijn: [http://www.lulu.com/product/paperback/introduction-to-high-performance-scientific-computing/14455750 Introduction to High Performance Scientific Computing] | ||
* Dongarra, Duff, Sorensen, van der Vorst: Numerical Linear Algebra for High-Performance Computers | * Dongarra, Duff, Sorensen, van der Vorst: Numerical Linear Algebra for High-Performance Computers | ||
Revision as of 10:49, 23 April 2018
- Term
- Summer 2018
- Lecturer
- Univ.-Prof. Dr. Daniel Kressner: John von Neumann Lecturer
- Time and Place
- Lecture: Monday, details see here
- Audience
- MA5328
- Master CSE
- Master Mathematics
- Topmath
- Master Informatics
- Master Mathematics in Data Science
- Master Data Engineering and Analytics
- Tutorials
- no tutorials
- Exam
- 60 minute written Exam or 20 minutes oral exam
- Semesterwochenstunden / ECTS Credits
- 2 SWS / 3 credits
- TUMonline
- https://campus.tum.de/tumonline/wblvangebot.wbshowlvoffer?ppersonnr=333087
News
The first lecture will be on Monday, 16.4.2018, 2pm (14:00) in room 02.08.020, M11.
The lecture dates have been fixed to 16.4., 23.4., 30.4., 14.5., 28.5., 4.6., 11.6., 18.6., 25.6., 2.7. (Monday 2pm)
See also TUMOnline at https://campus.tum.de/tumonline/wbLv.wbShowLVDetail?pStpSpNr=950377693&pSpracheNr=1
Contents
Low-rank compression is an ubiquitous tool in scientific computing and data analysis. There have been numerous exciting developments in this area during the last decade and the goal of this course is to give an overview of these developments, covering theory, algorithms, and applications of low-rank matrix and tensor compression. Specifically, the following topics will be covered:
1. Theory
- - Low-rank matrix and tensor formats (CP, Tucker, TT, hierarchical Tucker)
- - A priori approximation results
2. Algorithms
- - Basic operations with low-rank matrices and tensors
- - SVD-based compression
- - Randomized compression
- - Alternating optimization
- - Riemannian optimization
- - Nuclear norm minimization
- - Adaptive cross approximation and variants
3. Applications
- - Image processing
- - Matrix and tensor completion
- - Model reduction
- - Solution of large- and extreme-scale linear algebra problems from various applications (dynamics and control, uncertainty quantification, quantum computing, ...)
- - Tensors in deep learning
Depending on how the course progresses and the interest of the participants, hierarchical low-rank formats (HODLR, HSS, H matrices) may be covered as well.
Hands-on examples using publicly available software (in Matlab, Python, and Julia) will be provided throughout the course.
Lecture slides
- Slides 1: Basic concepts and subspace iteration lecture_1.pdf
- Slides 2:
Literature & external links
Pointers to the literature can be found in the slides.