Development of numerical methods for solving large-scale ill-conditioned linear system of equations and its applications
| Project/Area Number |
24560518
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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 |
Measurement engineering
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| Research Institution | University of Fukui |
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Principal Investigator |
HOSODA Yohsuke 福井大学, 工学(系)研究科(研究院), 教授 (80264951)
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| Co-Investigator(Kenkyū-buntansha) |
HASEGAWA Takemitsu 福井大学, 大学院工学研究科, 名誉教授 (70023314)
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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 |
¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
Fiscal Year 2014: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2013: ¥390,000 (Direct Cost: ¥300,000、Indirect Cost: ¥90,000)
Fiscal Year 2012: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
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| Keywords | 悪条件線形方程式 / 特異値分解 / QR分解 / ブロック化アルゴリズム / 悪条件問題 / 最小自乗問題 / グラム・シュミット法 / 大規模問題 / 反復解法 / 正則化法 / 逆問題 |
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| Outline of Final Research Achievements |
The purpose of our study is to develop new numerical methods for solving large-scale ill-conditioned linear system of equations. For dense matrices, numerical methods based on the singular value decomposition (SVD) have been used. However, these methods need high computational costs. To overcome such difficulties, we make use of numerical methods based on the QR decomposition instead of the SVD. We propose a new algorithm for efficiently computing the QR factorization of a given matrix. Our method uses a recursive blocked Gram-Schmidt orthogonalization and a recursive blocked Cholesky factorization. Numerical experiments show that our method is better than the conventional methods.
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Report
(4 results)
Research Products
(2 results)
