| Date | Topic(s) | Time | Zoom link |
Lecturer |
|---|---|---|---|---|
| 22.02 | Introduction to the course | 10:15-10:45 | https://uu-se.zoom.us/j/68666040360 | MN |
| Introduction to NLA, Basic iterative methods. Dense and sparse matrices, direct solution methods | Self reading | MN | ||
| "Hands-on" session 1: Ill-conditioning. Basic iterative methods here Files | ||||
| 23.02 | Discussion on the material and hands-on from 22.02. Projection methods - general framework, properties |
10:15-12:00 | https://uu-se.zoom.us/j/69558959957 | MN |
| Krylov subspace methods. Building Krylov subspaces. Arnoldi's method (slides) | 13:15-15:00 | https://uu-se.zoom.us/j/68758740248 | MN | |
| 25.02 | The conjugate gradient (CG) method - derivation, convergence rate estimates, influence of the type of the matrix spectrum on the convergence (slides) | 10:15-12:00 | https://uu-se.zoom.us/j/63152180134 | MN |
| The GMRES method - derivation, properties. Residual curves. Why Krylov subspaces? (slides) The Generalized Conjugate Gradient method (slides) | 13:15-15:00 | https://uu-se.zoom.us/j/63173467490 | MN | |
| "Hands-on" session 2: Iterative solution methods (here) Files |
| Date | Topic(s) | Time | Zoom link |
Lecturer |
|---|---|---|---|---|
| 1.03 | Add-ons: Pipelined versions of Krylov iteration methods (here). Preconditioning methods for sparse linear systems. (Block-)Incomplete factorizations | 10:15-12:00 | https://uu-se.zoom.us/j/63358720902 | MN |
| Preconditioning (cont): sparse approximate inverses, Domain Decomposition techniques, block-factorization-(Schur complement-)based preconditioning (slides ILU, SPAI, DD, Block-factorized) (hand-written block 2x2) (hand-written FEM element-by-element) | 13:15-15:00 | https://uu-se.zoom.us/j/63439361446 | MN | |
| 2.03 | (Nearly-)Optimal methods: (I) Multigrid and algebraic Multigrid techniques | 10:15-12:00 | https://uu-se.zoom.us/j/65838439509 | MN |
| (II) Algebraic Multilevel Iteration (AMLI) methods (here) | 13:15-15:00 | https://uu-se.zoom.us/j/67410085171 | MN | |
| "Hands-on" session 3: Preconditioning techniques. Multigrid and multilevel methods (here) (Files to be downloaded from the dropbox directory.) | ||||
| 4.03 | Least square problems, solution methods, CGLS (here) | 10:15-12:00 | https://uu-se.zoom.us/j/66121608352 | MN |
| Assignment 1 (here) (Files to be downloaded from the dropbox directory.) Deadline March 20, 2021 | MN |
| Date | Topic(s) | Time | Zoom link |
Lecturer |
|---|---|---|---|---|
| 8.03 | Structured dense matrices: Applications. Spectral properties of Toeplitz matrices (here) | 10:15-12:00 | https://uu-se.zoom.us/j/66406445680 | SSC |
| Band-preconditioning and spectral properties of the preconditioned matrices (here) | 13:15-15:00 | https://uu-se.zoom.us/j/64906919865 | SSC | |
| 9.03 | Matrix algebras; matrix algebra preconditioning; classical Korovkin Theorem (here) and (here) | 10:15-12:00 | https://uu-se.zoom.us/j/64273679672 | SSC | Korovkin theorem for matrix approximations (here) and (here) | 13:15-15:00 | https://uu-se.zoom.us/j/69574618519 | SSC |
| "Hands-on" session 4: Structured matrices | ||||
| Assignment no 2 here Deadline March 28, 2021 | MN |
| Date | Topic(s) | Time | Zoom link |
Lecturer |
|---|---|---|---|---|
| 15.03 | Basics. Eigenvalues, pseudo-eigenvalues, normal forms and perturbation theory. | 10:15-12:00 | https://uu-se.zoom.us/j/69827309400 | MN |
| Small eigenvalue problems. QR iteration | 13:15-15:00 | https://uu-se.zoom.us/j/66441063738 | MN | |
| 16.03 | Large eigenvalue problems, subspace methods. Lanczos and Arnoldi methods, implicit restarts (slides) (Jacobi-Davidson's method - self reading.) | 10:15-12:00 | https://uu-se.zoom.us/j/66261491459 | MN |
| Assignment no 3 here. Deadline April 11, 2021 |