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Low-rank approximation techniques

Objectives

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. The course aims at covering the following topics:

  • 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
  • Introduction to low-rank matrix and tensor manifolds
  • Selected other topics

Teacher

Prof. Dr. Daniel Kressner

Assistant

David Persson

Time Schedule

The first lecture and exercise will be on Thursday, September 22.

  • Lectures: Thursdays, 10h15 – 12h00, room GCA330
  • Exercises: Thursdays, 13h15 – 15h00, room MAA330
  • Please register on the Moodle page if you plan to attend the lectures.

Prerequisites

Numerical Analysis, Linear Algebra, knowledge of MATLAB, Julia, Python, or similar programming language

Lecture Material

The lecture material will appear on Moodle.

Useful Material