BEGIN:VCALENDAR VERSION:2.0 PRODID:-//Sabre//Sabre VObject 4.5.8//EN CALSCALE:GREGORIAN BEGIN:VTIMEZONE TZID:Europe/Zurich X-LIC-LOCATION:Europe/Zurich TZURL:http://tzurl.org/zoneinfo/Europe/Zurich BEGIN:DAYLIGHT TZOFFSETFROM:+0100 TZOFFSETTO:+0200 TZNAME:CEST DTSTART:19810329T020000 RRULE:FREQ=YEARLY;BYMONTH=3;BYDAY=-1SU END:DAYLIGHT BEGIN:STANDARD TZOFFSETFROM:+0200 TZOFFSETTO:+0100 TZNAME:CET DTSTART:19961027T030000 RRULE:FREQ=YEARLY;BYMONTH=10;BYDAY=-1SU END:STANDARD END:VTIMEZONE BEGIN:VEVENT UID:news1932@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20251204T113831 DTSTART;TZID=Europe/Zurich:20251209T121500 SUMMARY:Bernoullis Tafelrunde: Guifré Sánchez i Serra (EPFL) DESCRIPTION:The Density Matrix Renormalization Group algorithm (DMRG) is a popular alternating optimization scheme to solve high-dimensional eigenval ue problems arising in the context of quantum many-body systems. In recent years\, the development of several low-rank tensor formats has enabled th e design and analysis of new methods capable of approximating\, with high accuracy\, the solutions of such large-scale problems. One format that has proven particularly successful in tackling tensor-structured linear and e igenvalue problems is the tensor-train format\, introduced to the numerica l analysis community\, long after it had been known and used by the quantu m physics community under the name of matrix product states. The equivalen ce between these two notions has allowed for a more rigorous treatment of the DMRG algorithm\, which can now be understood as an alternating scheme for addressing general high-dimensional optimization problems.\\r\\nAlthou gh many convergence properties of DMRG remain poorly understood\, some sat isfactory results have been obtained regarding its local convergence behav ior. Thus\, in the first part of this talk\, I will introduce the main too ls involved in analyzing the local convergence properties of DMRG\, and ex tend these tools to obtain an analogous result for a recent parallel versi on of the algorithm\, inspired by two-level additive Schwarz methods.\\r\\ nThe search for a parallel version of DMRG is motivated by its inherently sequential nature\, which generally hinders efficient implementation on pa rallel computing architectures and thus limits its overall computational c ost. Related developments have recently demonstrated how to efficiently co nstruct algebraic two-level additive Schwarz preconditioners that signific antly accelerate iterative linear solvers such as CG. In the second part o f this talk\, I will give an overview of preconditioning strategies for (s ymmetric) eigenvalue problems\, discuss their impact on the convergence be havior of iterative eigensolvers (e.g. Jacobi–Davidson\, LOBPCG)\, and d escribe ongoing work aimed at adapting additive Schwarz ideas in this cont ext.\\r\\npdf_version [t3://file?uid=4087] X-ALT-DESC:

The Density Matrix Renormalization Group algorithm (DMRG) is a popular alternating optimization scheme to solve high-dimensional eigenv alue problems arising in the context of quantum many-body systems. In rece nt years\, the development of several low-rank tensor formats has enabled the design and analysis of new methods capable of approximating\, with hig h accuracy\, the solutions of such large-scale problems. One format that h as proven particularly successful in tackling tensor-structured linear and eigenvalue problems is the tensor-train format\, introduced to the numerical analysis community\, long after it had been known and used by t he quantum physics community under the name of matrix product states. The equivalence between these two notions has allowed for a more rigorous trea tment of the DMRG algorithm\, which can now be understood as an alternatin g scheme for addressing general high-dimensional optimization problems.

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Although many convergence properties of DMRG remain poorly understoo d\, some satisfactory results have been obtained regarding its local conve rgence behavior. Thus\, in the first part of this talk\, I will introduce the main tools involved in analyzing the local convergence properties of D MRG\, and extend these tools to obtain an analogous result for a recent pa rallel version of the algorithm\, inspired by two-level additive Schwarz m ethods.

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The search for a parallel version of DMRG is motivated by its inherently sequential nature\, which generally hinders efficient imple mentation on parallel computing architectures and thus limits its overall computational cost. Related developments have recently demonstrated how to efficiently construct algebraic two-level additive Schwarz preconditioner s that significantly accelerate iterative linear solvers such as CG. In th e second part of this talk\, I will give an overview of preconditioning st rategies for (symmetric) eigenvalue problems\, discuss their impact on the convergence behavior of iterative eigensolvers (e.g. Jacobi–Davidson\, LOBPCG)\, and describe ongoing work aimed at adapting additive Schwarz ide as in this context.

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pdf_version DTEND;TZID=Europe/Zurich:20251209T130000 END:VEVENT END:VCALENDAR