2011 Fiscal Year Final Research Report
The Solution of Least Squares Problems Using Krylov Subspace Methods
| Project/Area Number |
21560072
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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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) |
2009 – 2011
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| Keywords | 最小二乗問題 / 連立一次方程式 / 逆問題 / クリロフ部分空間法 / GMRES法 / 前処理 / 内部反復 / 共役勾配法 |
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| Research Abstract |
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. Such problems arise in science, engineering and sociology, for instance, in statistics, survey and control, where one develops a model equation which best fits observed data. 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.
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