Master 2024/2025

Computational Linear Algebra

Type: Compulsory course (Math of Machine Learning)

When: 1 year, 1, 2 module

Open to: students of one campus

Language: English

Course Syllabus

Abstract

Numerical linear algebra forms the basis for all modern computational mathematics. It is not possible to develop new large scale algorithms and even use existing ones without knowing it. In this course I will show, how numerical linear algebra methods and algorithms are used to solve practical problems. Matrix decompositions play the key role in numerical linear algebra. We will study different matrix decompositions in details: what are they, how to compute them efficiently and robustly, and most importantly, how they are applied to the solution of linear systems, eigenvalue problems and data analysis applications. For large-scale problems iterative methods will be described. I will try to highlight recent developments when it is relevant to the current lecture. This course should serve as a basis for other IT Skoltech courses. It will also serve as a first-time place where programming environment and infrastructure is introduced in a consistent manner.