Numerical Linear Algebra

Table of Contents

I am teaching this course in Spring 2025 and it is currently under development.

Course content

It is fair to say numerical linear algebra runs the world in our day and age. Examples of numerical algorithms relating to linear algebra that are a part of our daily lives are Fast Fourier Transform (mp3 and JPEG files) and Singular Value Decomposition (low rank approximation of matrices). From a scientific point, numerical linear algebra plays a central role in problems such as high-dimensional data analysis or in numerical solution of infinite-dimensional problems. The course will cover fundamentals of numerical linear algebra along with the essential algorithms. Topics include: singular value de- composition, QR algorithm, pivoting, least squares approximation, numerical stability, eigenvalue computation, iterative methods.

Lecture notes

You can navigate through the material including the lecture notes and supplementary Jupyter notebooks from the left pane. The materials follow the classical book by Trefethen & Bau.