Analysis and new developments on the novel iterative solvers for linear systems

2017 Fiscal Year Final Research Report

• Project/Area Number: 15K17498
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Computational science
• Research Institution: Tokyo City University (2017); Tokyo University of Science (2015-2016)
• Principal Investigator: Aihara Kensuke 東京都市大学, 知識工学部, 講師 (70735498)
• Research Collaborator: HOSODA Yohsuke 福井大学, 学術研究院工学系部門, 教授 ; SATO Hiroyuki 京都大学, 白眉センター, 助教
• Project Period (FY): 2015-04-01 – 2018-03-31
• Keywords: 大規模連立一次方程式 / 悪条件最小二乗問題 / クリロフ部分空間法 / 帰納的次元縮小法 / 丸め誤差解析 / 連続最適化 / シュティーフェル多様体 / ニュートン方程式

Outline of Final Research Achievements

Krylov subspace methods are extensively used as iterative solvers for large linear system of equations. In this study, we have given a rounding error analysis to the short recurrence Krylov subspace methods, and have proposed more effective algorithms than do the conventional ones. We have also worked on improving the convergence of the recent novel iterative solvers which are referred to as the induced dimension reduction (IDR)-type methods. Moreover, we have proposed efficient numerical solvers for the ill-conditioned least squares problems and for the optimization problems on Riemannian manifolds.

Free Research Field

計算科学，数値解析，数値線形代数