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NLA course in AI masters

Numerical Linear Algebra in AI Masters, Fall 2022

Date Lectures Practice sessions Home assignments
15.09.2022 General info about the course. Floating point numbers. Vector norms Review and main policies HW1
(Deadline: October, 4, 23:59 MSK)
22.09.2022 Matrix norms and unitary matrices Seminar 2
29.09.2022 Seminar 3
Seminar 4
HW2
(Deadline: October, 11, 23:59 MSK)
06.10.2022 Matrix rank and low-rank approximation. SVD.
Linear systems
13. 10.2022 Matrix multiplication and memory hierarchy. Seminar 5 HW3
(Deadline: October, 25, 23:59 MSK)
20.10.2022 Seminar 6
Seminar 7
27.10.2022 QR decomposition and how to compute it. Eigenvalues and eigenvectors. Schur decomposition.
QR algorithm. SVD and how we compute it.
03.11.2022 Seminars 8 and 9
10.11.2022 Sparse matrices and direct methods for large sparse linear systems. Spectral partitioning and Fiedler vector
Intro to iterative methods
17.11.2022 Great iterative methods Seminar 10
24.11.2022 Seminar 11
Seminar 12
HW4
(Deadline: December, 4, 23:59 MSK)
01.12.2022 Iterative methods and preconditioners Seminar 13
08.12.2022 Iterative methods for partial eigenvalue problem Seminar 14 HW5
(Deadline: December, 15, 23:59 MSK)
16.12.2022 Structured matrices, convolutions, FFT, Toeplitz matrices
Matrix functions and randomized methods in NLA