Iterative Methods for Least Squares Problems and their Application to Inverse Problems
| Project/Area Number |
24560082
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Engineering fundamentals
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| Research Institution | National Institute of Informatics |
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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)
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| Project Period (FY) |
2012-04-01 – 2015-03-31
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| Project Status |
Completed (Fiscal Year 2014)
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| Budget Amount *help |
¥5,070,000 (Direct Cost: ¥3,900,000、Indirect Cost: ¥1,170,000)
Fiscal Year 2014: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2013: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2012: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
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| 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 / 反復法 / 線形計画問題 / 特異系 / 非線形最小二乗問題 / 制約付き最小二乗問題 / 薬物動態 / 内部反復 / 画像再構成 |
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| 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.
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Report
(4 results)
Research Products
(51 results)
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[Presentation] Inner-iteration preconditioning for CG and MINRES-type methods,2014
Author(s)
Morikuni, K., Rozloznik, M., and Hayami, K.,
Organizer
The Fifth International Conference on Numerical Algebra and Scientific Computing (NASC 2014),
Place of Presentation
Tongji University, Shanghai, China
Year and Date
2014-10-25 – 2014-10-29
Related Report
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[Presentation] Improvements to the Cluster Newton Method for Underdetermined Inverse Problems2014
Author(s)
Gaudreau, P., Hayami, K., Aoki, Y., Safoui, H., and Konagaya, A.,
Organizer
生命医薬情報学連合大会(IIBMP2014),
Place of Presentation
仙台国際センター(宮城県仙台市）
Year and Date
2014-10-02 – 2014-10-04
Related Report
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[Presentation] The Cluster Newton Method and its Improvement for Underdetermined Inverse Problems2014
Author(s)
Aoki, Y., Gaudreau, P., Hayami, K.*, De Sterck, H., Safouhi, H., and Konagaya, A.,
Organizer
Institute of Computational Mathematics and Scientific/Engineering Computing, Chinese Academy of Sciences
Place of Presentation
Institute of Computational Mathematics and Scientific/Engineering Computing, Chinese Academy of Sciences, Beijing, China
Year and Date
2014-07-14
Related Report
Invited
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[Presentation] Sampling families of solutions using the Cluster Newton method for an underdetermined inverse problem: Parameter identification for pharmacokinetics2013
Author(s)
Gaudreau, P., Hayami, K., Aoki, Y., Safouhi, H., and Konagaya, A.
Organizer
Recent Developments in Numerical Methods for Seismic Inverse Problems & Applications
Place of Presentation
University of Calgary, Canada
Related Report
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[Presentation] Improvements to the Cluster Newton Method for Underdetermined Inverse Problems -Pararameter Identification for Pharmacokinetics-2013
Author(s)
Latt, K. M.-M., Gaudreau, P.J., Hayami, K., Aoki, Y., Safoui, H. and Konagaya, A.,
Organizer
CBI学会2013年大会-生命医薬情報学連合大会-, Poster presentation, C-4-05
Place of Presentation
タワーホール船堀, 東京
Related Report
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[Presentation] 最小二乗問題と反復解法
Author(s)
速水 謙, 保國惠一
Organizer
日本応用数理学会 3部会連携応用数理セミナー
Place of Presentation
東京大学工学部
Related Report
Invited
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