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2020-02-25 Per Christian Hansen教授による講演会(その1)

投稿者:  相原 研輔(東京都市大学)
会場: 一橋大学 一橋講堂 2階 中会議室3
概要: Per Christian Hansen教授(デンマーク工科大学)をお招きし「Hybrid Enriched Bidiagonalization for Discrete Ill-Posed Problems」という題目でご講演頂きます.本件は東京で開催する3つの講演会の1つ目です.

日程 2020年 2月25日(火)2:00PM-3:00PM
会場 国立情報学研究所(アクセス) 12階1212室 大学院講義室1

一橋大学 一橋講堂 2階 中会議室3 (access) /
Hitotsubashi University, National Center of Sciences Building, 2F, Medium Conference Room 3 (access)

* 会場が変更されました/the venue was changed
本文 この度,デンマーク工科大学のPer Christian Hansen教授をお招きし, 下記の講演会を開催することとなりました. ご興味のある方は是非ご参加ください.
本件は東京で開催する3つの講演会の1つ目です. 他2件は, 同日同会場にて, および, 2月26日に東京都市大学にて開催されます.

This lecture is supported by Invitational Fellowships for Research in Japan (Short-term S).
Speaker Professor Per Christian Hansen
(DTU Compute, Technical University of Denmark), http://www2.compute.dtu.dk/~pcha/
Title Hybrid Enriched Bidiagonalization for Discrete Ill-Posed Problems
Abstract Solution of large-scale inverse problems call for the use of iterative methods. The regularizing property of the Golub-Kahan bidiagonalization algorithm is powerful when the associated Krylov subspace captures the dominating components of the solution. In some applications, we can further improve the regularized solution by means of enrichment, that is, by augmenting the Krylov subspace with a low-dimensional subspace that represents specific prior information.

Building on earlier work on Augmented GMRES and Enriched CGNR - by Calvetti & Reichel and ourselves - we demonstrate how to carry these ideas over to the bidiagonalization algorithm, and we describe how to incorporate Tikhonov regularization. This leads to a hybrid iterative method where the choice of the regularization parameter in each iteration also provides a stopping rule for the iterations.

In this talk, I will briefly survey the regularizing properties of the Krylov subspace methods, and then motivate and present our new algorithm. I will discuss some implementation details, and illustrate the algorithm with numerical examples.

This is joint work with Kuniyoshi Abe and Yiqiu Dong.
問い合わせ先 阿部 邦美,速水 謙
e-mail: abe@gifu.shotoku.ac.jp , hayamiseparatornii.ac.jp