MATH-403 / 5 crédits

Enseignant:

Langue: Anglais

Remark: pas donné en 2021-22


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

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:

  • Choose a suitable low-rank approximation techniques for treating a large-scale problem or high-dimensional data
  • Analyze algorithms for low-rank approximation
  • Prove fundamental results in low-rank approximation
  • Implement low-rank approximation algorithms

Transversal skills

  • Plan and carry out activities in a way which makes optimal use of available time and other resources.
  • Use a work methodology appropriate to the task.
  • Assess one's own level of skill acquisition, and plan their on-going learning goals.
  • Demonstrate a capacity for creativity.
  • Write a scientific or technical report.

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

Dans les plans d'études

  • Semestre: Automne
  • Forme de l'examen: Oral (session d'hiver)
  • Matière examinée: Low-rank approximation techniques
  • Cours: 2 Heure(s) hebdo x 14 semaines
  • Exercices: 2 Heure(s) hebdo x 14 semaines
  • Semestre: Automne
  • Forme de l'examen: Oral (session d'hiver)
  • Matière examinée: Low-rank approximation techniques
  • Cours: 2 Heure(s) hebdo x 14 semaines
  • Exercices: 2 Heure(s) hebdo x 14 semaines
  • Semestre: Automne
  • Forme de l'examen: Oral (session d'hiver)
  • Matière examinée: Low-rank approximation techniques
  • Cours: 2 Heure(s) hebdo x 14 semaines
  • Exercices: 2 Heure(s) hebdo x 14 semaines
  • Semestre: Automne
  • Forme de l'examen: Oral (session d'hiver)
  • Matière examinée: Low-rank approximation techniques
  • Cours: 2 Heure(s) hebdo x 14 semaines
  • Exercices: 2 Heure(s) hebdo x 14 semaines
  • Semestre: Automne
  • Forme de l'examen: Oral (session d'hiver)
  • Matière examinée: Low-rank approximation techniques
  • Cours: 2 Heure(s) hebdo x 14 semaines
  • Exercices: 2 Heure(s) hebdo x 14 semaines
  • Semestre: Automne
  • Forme de l'examen: Oral (session d'hiver)
  • Matière examinée: Low-rank approximation techniques
  • Cours: 2 Heure(s) hebdo x 14 semaines
  • Exercices: 2 Heure(s) hebdo x 14 semaines

Semaine de référence

 LuMaMeJeVe
8-9     
9-10     
10-11     
11-12     
12-13     
13-14     
14-15     
15-16     
16-17     
17-18     
18-19     
19-20     
20-21     
21-22