Iterative Methods for Least Squares Problems and their Application to Inverse Problems

2014 Fiscal Year Final Research Report

• Project/Area Number: 24560082
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Engineering fundamentals
• Research Institution: National Institute of Informatics
• Principal Investigator: HAYAMI Ken 国立情報学研究所, 情報学プリンシプル研究系, 教授 (20251358)
• Project Period (FY): 2012-04-01 – 2015-03-31
• Keywords: 最小二乗問題 / 連立一次方程式 / 逆問題 / 反復解法 / クリロフ部分空間法 / 前処理 / GMRES法 / 内部反復法

Outline of Final Research Achievements

Least squares problems arise, for instance, when one wants to find a solution to system of linear equations where there are more equations than unknowns. They are fundamental problems in science and engineering etc. In this research, we developed a new method to solve large and difficult least squares problems efficiently and accurately using an iterative scheme. We demonstrated the effectiveness of the method by numerical experiments and theory. Further, we developed methods for solving problems with constraints on the unknowns, and also nonlinear problems. We also developed methods for solving inverse problems where the parameters of how medicine becomes effective in the patient's body, from how the excretion varies with time.

Free Research Field

数値解析, 数値線形代数, 逆問題