Numerical linear algebra course, @SkolTech, Term 2, 2022

This repository contains lectures and homeworks for Numerical linear algebra course. It will be updated as the class progresses.

| Week | Lecture notebooks | Supplementary materials | Homework | Tests | |:------:|:----------|:----------:|:----------:|-------| |1| General info [GitHub] <br> Lecture 1. Floating point arithmetic, vector norms [GitHub] <br> Lecture 2. Matrix norms and unitary matrices [GitHub] <br> Lecture 3. Memory hierarchy, matrix multiplication, Strassen algorithm [Github]| | HW1 <br> (Deadline: November, 20, 23:59 MSK) | | 2 | Lecture 4. Pytorch and Jax tutorials. <br> Lecture 5. Matrix rank, skeleton decomposition, SVD. [GitHub] <br> Lecture 6. Linear systems [GitHub] | JAX Tutorial [GitHub] <br> PyTorch Tutorial [GitHub] | | | 3 | Lecture 7. Eigenvalues and eigenvectors. [GitHub] <br> Lecture 8. Matrix decompositions and how we compute them [GitHub] <br> Lecture 9. Symmetric eigenvalue problem and SVD [GitHub] | | | | 4 | Lecture 10. Randomized linear algebra [GitHub] <br> Lecture 11. From dense to sparse linear algebra [GitHub] <br> Lecture 12. Midterm Exam | | HW2 <br> (Deadline: December, 11, 23:59 MSK) | | 5 | Lecture 13. Sparse direct solvers [GitHub] <br> Lecture 14. Intro to iterative methods [Github] <br> Lecture 15. Great iterative methods [Github] | | | | 6 | Lecture 16. Iterative methods and preconditioners [Github] <br> Lecture 17. Structured matrices, FFT, convolutions, Toeplitz matrices [Github] <br> Lecture 18. Iterative methods for large scale eigenvalue problems [Github] | | | | 7 | Lecture 19. Matrix functions and matrix equations [Github] <br> Lecture 20. Tensors and tensor decompositions [Github] <br> Lecture 21. Final Exam (day 1) | | | Exam questions <br> Theoretical minimum questions | 8 | Lecture 22. Final Exam (day 2) <br> Lecture 23. Project Presentation (day 1) <br> Lecture 24. Project Presentation (day 2) | | |