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SUMMARY:SHORT Course: Introduction to randomized numerical linear algebra
DTSTART;VALUE=DATE-TIME:20260414T140000Z
DTEND;VALUE=DATE-TIME:20260417T203000Z
DTSTAMP;VALUE=DATE-TIME:20260403T201100Z
UID:indico-event-938@indico.gssi.it
CONTACT:nicola.guglielmi@gssi.it\;alice.cortinovis@unipi.it
DESCRIPTION:LecturerAlice Cortinovis alice.cortinovis@unipi.itTimetable an
 d workloadLectures: 8 hoursComputational session: 2 hoursCourse contentThi
 s course provides an introduction to the field of randomized numerical lin
 ear algebra. As problem dimensions grow\, classical deterministic numerica
 l linear algebra algorithms often become prohibitively expensive in terms 
 of computational cost or memory usage. Randomization provides a powerful a
 lternative and allows us to design algorithms that are both computationall
 y efficient and provably accurate with high probability. The goal of the c
 ourse is to present the key mathematical principles underlying randomized 
 matrix algorithms\, emphasizing both the theoretical analysis and some pra
 ctical numerical considerations.We start with a discussion of several reas
 ons why randomization helps numerical linear algebra algorithms to be fast
 er while retaining accuracy. As a first example\, we study stochastic trac
 e estimation\, which serves as a motivation to study concentration inequal
 ities for random variables and matrices. We introduce subspace embeddings\
 , which are a way to reduce high-dimensional problems to low-dimensional o
 nes while approximately preserving the geometrical structure. This powerfu
 l concept is applied to the solution of overdetermined least-squares probl
 ems. We then discuss the workhorse of randomized numerical linear algebra:
  the randomized rangefinder for the solution of low-rank approximation pro
 blems. The course also covers other related kinds of low-rank approximatio
 ns\, such as Nyström approximations for symmetric positive semidefinite m
 atrices and approximations based on the selection of rows and columns. At 
 the end of the course\, participants will see some of the algorithms at wo
 rk in a "hands-on" computational session.Course requirementsThe course is 
 intended for students with knowledge of linear algebra and basic probabili
 ty theory. Familiarity with numerical linear algebra (least-squares proble
 ms\, standard matrix factorizations) is desirable. The necessary elements 
 of numerical linear algebra will be briefly reviewed before introducing th
 eir randomized counterparts. Referenceshttps://doi.org/10.1017/S096249292
 0000021 \n\nhttps://indico.gssi.it/event/938/
URL:https://indico.gssi.it/event/938/
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