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SUMMARY:INdAM Workshop: Low-rank Structures and Numerical Methods in Matri
 x and Tensor Computations
DTSTART:20250831T000000Z
DTEND:20250905T150000Z
DTSTAMP:20260518T211600Z
UID:indico-event-307@events.dm.unipi.it
DESCRIPTION:Speakers: Cecilia Pagliantini (University of Pisa)\, Valeria S
 imoncini (Universita' di Bologna)\, Davide Palitta (Alma Mater Studiorum\,
  Università di Bologna)\, Michele Benzi (Scuola Normale Superiore)\, Beat
 rice Meini (University of Pisa)\, Fabio Durastante (Università di Pisa)\n
 \nNumerical (multi-)linear algebra is central to many computational method
 s for complex networks\, stochastic processes\, machine learning\, and num
 erical solution of PDEs. The matrices (or tensors) encountered in applicat
 ions are often rank-structured: approximately low-rank\, or with low-rank 
 blocks\, or low-rank modifications of “simpler” matrices. Identifying 
 and exploiting rank structure is crucial for achieving optimal performance
  and for making data interpretations feasible by means of the most insight
 ful multi-array representation.A common example is given by the low-rank a
 pproximation of a given matrix\, for which the singular value decompositio
 n (SVD) is classically employed. For large dimensions\, this approach is u
 nfeasible both in terms of computational costs and memory requirements. Th
 is problem is particularly crucial when dealing with the huge amount of da
 ta currently processed by data science algorithms. Alternatives have been 
 designed to overcome the SVD drawbacks. These include variants of the Lanc
 zos method and adaptive cross approximation.Recently\, randomized methods 
 have gained traction\, being more robust than the aforementioned approache
 s. They only require a few matrix-vector products\, and the acceptance of 
 a failure probability\, that can be made arbitrarily small by slightly inc
 reasing the cost of the method. The analogous problem for tensors (arrays 
 with more than 2 indices) is much harder. No explicit solution is availabl
 e for the best approximant (when it exists)\, as no direct analogue of the
  SVD is known. For this reason\, compression strategies have been proposed
  over the years.If a computational problem can be reduced to an easier sub
 problem by a low-rank correction\, often we can solve the simple problem f
 irst\, and then reconstruct only the difference with the actual solution i
 n the form of a low-rank update. Array structures\, in the form of matrix 
 and tensor equations\, also naturally stem from the computational treatmen
 t of many application problems governed by steady-state or time-dependent 
 partial differential equations\, where the array form allows to preserve i
 mportant structural properties of solutions such as symmetry and definiten
 ess\, even at low accuracies.Low-rank structure plays a crucial role also 
 in many other areas. Network science problems\, such as clustering and com
 munity detection and the construction of preconditioners for solving netwo
 rk-related linear systems\, can also be tackled using low-rank approximati
 on techniques\, but little work has been done so far in this direction.Wor
 kshop ScheduleThe workshop will take place from the morning of Monday\, Se
 ptember 1st\, to the afternoon of Friday\, September 5th. Participants are
  expected to register and arrive on the afternoon of Sunday\, August 31st.
 Scientific CommitteeMichele BenziBeatrice MeiniValeria SimonciniOrganizing
  CommitteeFabio DurastanteCecilia PagliantiniDavide PalittaSponsors \n\nh
 ttps://events.dm.unipi.it/event/307/
LOCATION:Palazzone di Cortona
URL:https://events.dm.unipi.it/event/307/
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