Coursebooks 2018-2019

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Low-rank approximation techniques

MATH-403

Lecturer(s) :

Kressner Daniel

Language:

English

Summary

Low-rank approximation techniques have become a key tool in scientific computing to deal with large-scale problems and high-dimensional data. This course covers state-of-the-art algorithms and current research in this area.

Content

- Theoretical background of low-rank matrix approximation
- Subspace iteration
- Randomized low-rank approximation
- Low-rank approximation by deterministic column/row selection
- Low-rank approximation by randomized sampling
- Basic introduction to tensors
- Tensor rank, CP, Tucker, and TT decompositions of tensors
- Alternating least-squares algorithms
- Riemannian optimization on low-rank matrix and tensor manifolds

Keywords

numerical algorithms, linear algebra, matrix, tensor, random vectors, high dimensions, low rank

Learning Prerequisites

Required courses

Linear Algebra, Numerical Analysis

Recommended courses

Probability theory

Important concepts to start the course

Programming in Matlab, Python, Julia, or a similar language.

Learning Outcomes

By the end of the course, the student must be able to:

Transversal skills

Teaching methods

Lectures and exercises.

Expected student activities

Attending lectures, exercises, and doing a mini-project.

Assessment methods

Oral exam covering key concepts of the course. During the oral exam, the mini-project, which accounts for 20% of the grade, will be evaluated.

Supervision

Office hours No
Assistants Yes
Forum No

Resources

Bibliography

References to the current literature will be provided in the slides and lecture notes. Many of the linear algebra foundations of this course are contained in Horn/Johnson: Matrix Analysis, 2nd edition, CUP, 2012.

Références suggérées par la bibliothèque
Notes/Handbook

Detailed slides and lecture notes will be provided as the course progresses.

Websites

In the programs

Reference week

 MoTuWeThFr
8-9 MAA110   
9-10    
10-11 MAA110   
11-12    
12-13     
13-14     
14-15     
15-16     
16-17     
17-18     
18-19     
19-20     
20-21     
21-22     
 
      Lecture
      Exercise, TP
      Project, other

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  • Autumn semester
  • Winter sessions
  • Spring semester
  • Summer sessions
  • Lecture in French
  • Lecture in English
  • Lecture in German