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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
  • Riemannian optimization on low-rank matrix and tensor manifolds

Teacher

Prof. Dr. Daniel Kressner

Assistant

Dr. Lana Perisa

Time Schedule

The first lecture and exercise will be on Tuesday, September 25.

  • Lectures: Tuesdays, 8h15 – 10h00, room MAA110
  • Exercises: Tuesdays, 10h15 – 12h00, room MAA110

Prerequisites

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

Lecture Material

Draft of Lecture Notes

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Exercises

Mini-projects

Useful Material

Exam topics