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:news995@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20200317T094313 DTSTART;TZID=Europe/Zurich:20200312T161500 SUMMARY:CANCELLED: Perlen-Kolloquium: Prof. Dr. Martin J. Gander (Universit é de Genève) DESCRIPTION:Das Perlen-Kolloquium am 12. März 2020 wird nicht stattfinden. \\r\\nIterative methods for linear systems were invented for the same reas ons as they are used today\, namely to reduce computational cost. Gauss st ates in a letter to his friend Gerling in 1823: "you will in the future ha rdly eliminate directly\, at least not when you have more than two unknown s". Richardson's paper from 1910 was then very influential\, and is a mode l of a modern numerical analysis paper: modeling\, discretization\, approx imate solution of the discrete problem\, and a real application. More gene ral vector extrapolation methods were then introduced and studied in the p ioneering work of Bresinzki\, and they can be shown to be equivalent to Kr ylov method. It was however the work of Stiefel\, Hestenes and Lanczos in the early 1950 that sparked the success story of Krylov methods with the i nvention of the conjugate gradient method\, and there are now many Krylov methods to choose from. For general linear systems\, they come in two main classes\, the ones that minimize the residual in a Krylov space\, and the ones that make the residual orthogonal to it. This will bring us finally to the modern iterative methods for solving partial differential equations \, which also come in two main classes: domain decomposition methods and m ultigrid methods. Domain decomposition methods go back to the alternating Schwarz method invented by Herman Amandus Schwarz in 1869 to close a gap i n the proof of Riemann's famous Mapping Theorem. Multigrid goes back to th e seminal work by Fedorenko in 1961\, with main contributions by Brandt an d Hackbusch in the Seventies. X-ALT-DESC:

Das Perlen-Kolloquium am 12. März 2020 wird nicht stattfi nden.

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Iterative methods for linear systems were invented for t he same reasons as they are used today\, namely to reduce computational co st. Gauss states in a letter to his friend Gerling in 1823: "\;you wil l in the future hardly eliminate directly\, at least not when you have mor e than two unknowns"\;. Richardson's paper from 1910 was then very inf luential\, and is a model of a modern numerical analysis paper: modeling\, discretization\, approximate solution of the discrete problem\, and a rea l application. More general vector extrapolation methods were then introdu ced and studied in the pioneering work of Bresinzki\, and they can be show n to be equivalent to Krylov method. It was however the work of Stiefel\, Hestenes and Lanczos in the early 1950 that sparked the success story of K rylov methods with the invention of the conjugate gradient method\, and th ere are now many Krylov methods to choose from. For general linear systems \, they come in two main classes\, the ones that minimize the residual in a Krylov space\, and the ones that make the residual orthogonal to it. Thi s will bring us finally to the modern iterative methods for solving partia l differential equations\, which also come in two main classes: domain dec omposition methods and multigrid methods. Domain decomposition methods go back to the alternating Schwarz method invented by Herman Amandus Schwarz in 1869 to close a gap in the proof of Riemann's famous Mapping Theorem. M ultigrid goes back to the seminal work by Fedorenko in 1961\, with main co ntributions by Brandt and Hackbusch in the Seventies.

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