他組織イベント案内

2019-03-06 Reichel教授による講演会

投稿者:  速水 謙(国立情報学研究所)
会場: 国立情報学研究所 12F, Room 1212 (Lecture Room 1)
概要: 線形離散不適切問題に対するArnoldi分解, GMRES, 前処理

日程 2019年 3月 6日(水) / March 6th(Wed)
11:00-12:00
会場 国立情報学研究所 12F, Room 1212 (Lecture Room 1) / National Institute of Informatics, 12F, Room 1212 (Lecture Room 1)
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Speaker Professor Lothar Reichel
Department of Mathematical Sciences, Kent State University, OH, USA
Title The Arnoldi decomposition, GMRES, and preconditioning for linear discrete ill-posed problems
Abstract GMRES is one of the most popular iterative methods for the solution of large linear systems of equations that arise from the discretization of linear well-posed problems, such as boundary value problems for elliptic partial differential equations. The method is also applied to the iterative solution of linear systems of equations that are obtained by discretizing linear ill-posed problems, such as many inverse problems.
However, GMRES does not always perform well when applied to the latter kind of problems.
This talk seeks to shed some light on reasons for the poor performance of GMRES in certain situations, and discusses some remedies based on specific kinds of preconditioning. The standard implementation of GMRES is based on the Arnoldi process, which also can be used to define a solution subspace for Tikhonov or TSVD regularization, giving rise to the Arnoldi-Tikhonov and Arnoldi-TSVD methods, respectively. The performance of the GMRES and the latter methods is discussed.
Organizer Ken Hayami (National Institute of Informatics)
問い合わせ先 速水 謙
〒101-8430 東京都 千代田区 一ツ橋 2-1-2 国立情報学研究所
e-mail: hayamiseparatornii.ac.jp
詳細 web https://www.nii.ac.jp/en/event/2019/0306.html