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:news1464@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20230509T105935 DTSTART;TZID=Europe/Zurich:20230512T110000 SUMMARY:Seminar in Numerical Analysis: Martin Eigel (WIAS Berlin) DESCRIPTION:Weighted least squares methods have been examined thouroughly t o obtain quasi-optimal convergence results for a chosen (polynomial) basis of a linear space. A focus in the analysis lies on the construction of op timal sampling measures and the derivation of a sufficient sample complexi ty for stable reconstructions. When considering holomorphic functions such as solutions of common parametric PDEs\, the anisotropic sparsity they ex hibit can be exploited to achieve improved results adapted to the consider ed problem. In particular\, the sparsity of the data transfers to the solu tion sparsity in terms of polynomial chaos coefficients. When using nonlin ear model classes\, it turns out that the known results cannot be used dir ectly. To obtain comparable a priori rates\, we introduce a new weighted v ersion of Stechkin's lemma. This enables to obtain optimal complexity resu lts for a model class of low-rank tensor trains. We also show that the sol ution sparsity results in sparse component tensors and sketch how this can be realised in practical algorithms. A nice application is the reconstruc tion of Galerkin solutions for parametric PDEs. With this\, a provably con verging a posteriori adaptive algorithm can be derived for linear model PD Es with non-affine coefficients.\\r\\n\\r\\nFor further information about the seminar\, please visit this webpage [t3://page?uid=1115]. X-ALT-DESC:

Weighted least squares methods have been examined thouroughly to obtain quasi-optimal convergence results for a chosen (polynomial) bas is of a linear space. A focus in the analysis lies on the construction of optimal sampling measures and the derivation of a sufficient sample comple xity for stable reconstructions. When considering holomorphic functions su ch as solutions of common parametric PDEs\, the anisotropic sparsity they exhibit can be exploited to achieve improved results adapted to the consid ered problem. In particular\, the sparsity of the data transfers to the so lution sparsity in terms of polynomial chaos coefficients. When using nonl inear model classes\, it turns out that the known results cannot be used d irectly. To obtain comparable a priori rates\, we introduce a new weighted version of Stechkin's lemma. This enables to obtain optimal complexity re sults for a model class of low-rank tensor trains. We also show that the s olution sparsity results in sparse component tensors and sketch how this c an be realised in practical algorithms. A nice application is the reconstr uction of Galerkin solutions for parametric PDEs. With this\, a provably c onverging a posteriori adaptive algorithm can be derived for linear model PDEs with non-affine coefficients.

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For further information about the seminar\, please visit this webpage.

DTEND;TZID=Europe/Zurich:20230512T120000 END:VEVENT END:VCALENDAR