| Time | Monday | Tuesday | Wednesday | Thursday | Friday |
|---|---|---|---|---|---|
| 07:00–08:30 | Breakfast | ||||
| 08:30–10:00 | Arrival | Lecture 3 (Alice) | Lecture 5 (Hussam) | Lecture 8 (Alice) | Lecture 12 (Yuji) |
| 10:00–10:30 | Icebreaker | Coffee Break | |||
| 10:30–12:00 | Lecture 1 (Daniel) | Lecture 4 (Afonso) | Lecture 6 (Laura) | Lecture 9 (Yuji) | Lecture 13 (Daniel) and Q&A |
| 12:00–14:00 | Lunch | ||||
| 14:00–15:30 | Lecture 2 (Daniel) | Excursion | Lecture 7 (Laura) | Lecture 10 (Hussam) | |
| 15:30–16:00 | Coffee Break | Coffee Break | |||
| 16:00–17:30 | Student talks/posters | Industry event | Lecture 11 (Yuji) | ||
| 18:00–20:00 | Dinner | Dinner | Evening Activities | ||
| 20:00–22:00 | Evening Activities | Dinner | Evening Activities | Dinner | |
Lectures
Each lecture is 90 minutes long and includes a 10-minute break.
Lecturer: Daniel Kressner
Content: Key computational tasks in NLA, matrix access models, random vectors, expectation and concentration, JL and OSE, sketch-and-solve linearleast squares, randomized range finding.
Lecturer: Alice Cortinovis
Content: Girard-Hutchinson estimator with analysis (Chernoff bounds, concentration inequalities for sub-Gaussian / sub-Gamma / (sub-exponential) random variables), variance reduction techniques (Hutch++, XTrace).
Slides: Slides
Lecturer: Afonso Bandeira
Content: How free probability can help with getting sharper non-asymptotic control of random matrices that appear in RLA.
Slides: Slides
Lecturer: Hussam al Daas
Content: CP, Tucker and Tensor Train. Matrices with columns formed as vectorized structured low-rank tensors including KRP, Tucker and TT.
Slides: Slides
Lecturer: Laura Grigori
Content: Oblique versus orthogonal projections, Randomized GS, Householder, Cholesky QR. Randomized Krylov for linear systems and eigenvalue problems, randomized DLRA.
Lecturer: Alice Cortinovis
Content: Nyström and CUR (cross approximation): existence result with maximum volume, greedy ACA
algorithm ↔ Gaussian elimination, diagonal pivoting for SPSD matrices, randomly pivoted Cholesky. Column subset selection problem: existence result with volume sampling, expensiveness of exact volume sampling, QR with column pivoting (also randomized version), ARP.
Slides: Slides
Lecturer: Yuji Nakatsukasa
Content: Variants CC†A, AR†R, CUR with various choices of U. Fundamental theorem (accuracy bound). A posteriori error estimate. CUR computation: sketching for pivoting, iterativeCUR. Connections with CUR: LU, Chebyshev interpolation. DEIM. Leverage score sampling, subsampled least-squares problems. CUR for parameter-dependent problems (low-rank approx, linear systems). Kaczmarz methods.
Slides: Slides
Lecturer: Hussam al Daas
Content: Optimzation (trust and norm regularization). Low-rank structure in imaging applications.
Slides: Slides
Lecturer: Yuji Nakatsukasa
Content: Forward vs. backward stability. Backward stability of orthogonal linear algebra. Generalized Nystrom, Nystrom, preconditioned least-squares problems, preconditioned linear system solver, error certificates, SMW, MINBERR.
Slides: Slides
Excursion
Excursion in the region around Murten/Morat for all participants of the summer school.
Industry event
Round-table discussion involving our sponsors and representatives from academia.
Evening activities
Diverse social, cultural, or sporty activities proposed by the organizers or participants.