* Dates within the next 7 days are marked by a star.
Anna-Mariya Otsetova (Midterm review)
Quantitative asymptotics for stochastic evolution equations
* Friday 25 April 2025, 11:15, M3 (M234)
Eero Virmavirta
Optimizing application placement in private cloud environment under capacity constraints (MSc thesis presentation)
* Monday 28 April 2025, 15:00, M2 (M233)
SAL Seminar
Aapo Pulkkinen
TBA
Wednesday 07 May 2025, 10:15, M3 (M234)
Seminar on analysis and geometry
Olavi Nevanlinna
Low rank perturbation and Krylov methods
Wednesday 07 May 2025, 14:00, M2 (M233)
We discuss bounds for Krylov methods which are robust in low rank perturbation of the preconditioner.
We first demonstrate using two examples where the spectra are known the different roles of the spectrum and the decay of singular values have in the speed of the iterative processes. Recall that while the spectrum can move dramatically, the singular values do not, and the convergence speed is essentially determine by the decay of singular values.
In the first example a unitary matrix is rank-one perturbation of a nilpotent one and in the second a self-adjoint compact operator is rank-one perturbation of a quasinilpotent one.
Considering the resolvent as a meromorphic function rather than just analytic outside the spectrum it is possible to to show that the behavior seen in those examples is true in general, without assuming anything about how the spectrum moves under the low rank perturbation.
Numerical Analysis seminar
Petteri Kaski
Kronecker scaling of tensors with applications to arithmetic circuits and algorithms
Thursday 15 May 2025, 14:15, M2 (M233)
We show that sufficiently low tensor rank for the balanced tripartitioning tensor $P_d(x,y,z)=\sum_{A,B,C\in\binom{[3d]}{d}:A\cup B\cup C=[3d]}x_Ay_Bz_C$ for a large enough constant $d$ implies uniform arithmetic circuits for the matrix permanent that are exponentially smaller than circuits obtainable from Ryser's formula. We show that the same low-rank assumption implies exponential time improvements over the state of the art for a wide variety of other related counting and decision problems.
As our main methodological contribution, we show that the tensors $P_n$ have a desirable Kronecker scaling property: They can be decomposed efficiently into a small sum of restrictions of Kronecker powers of $P_d$ for constant $d$. We prove this with a new technique relying on Steinitz's lemma, which we hence call Steinitz balancing.
As a consequence of our methods, we show that the mentioned low rank assumption (and hence the improved algorithms) is implied by Strassen's asymptotic rank conjecture [Progr. Math. 120 (1994)], a bold conjecture that has recently seen intriguing progress.
Joint work with Andreas Björklund, Tomohiro Koana, and Jesper Nederlof; cf. https://arxiv.org/abs/2504.05772.
ADM Seminar
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