2022 Fiscal Year Final Research Report
Research on the development of fast and robust algorithms for large-scale eigenvalue problems
| Project/Area Number |
17K14143
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Computational science
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| Research Institution | Hosei University (2018-2022)
The University of Tokyo (2017) |
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Principal Investigator |
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| Project Period (FY) |
2017-04-01 – 2023-03-31
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| Keywords | 数値線形代数 |
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| Outline of Final Research Achievements |
In this study, numerical algorithms for eigenvalue problems have been designed from the viewpoint of applying matrix factorization approach and projection techniques in matrix calculations. Specifically, a new fast iterative improvement method is proposed as a result of joint research with Prof. Ogita of Tokyo Woman's Christian University. In addition, fast, accurate, and robust numerical algorithms for important mathematical problems in many application areas have been provided, where they can be regarded as variants of the eigenvalue problem.
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| Free Research Field |
数値解析
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| Academic Significance and Societal Importance of the Research Achievements |
インターネット上のウェブ検索のシステムや，購買のための情報推薦システムは，数理的には行列に関する数値計算に帰着される．行列に関する数値計算の中でも，固有値計算は一つの柱をなす重要なものである．本研究は，固有値計算の計算技術の開発とともに，その計算技術の応用範囲を今以上に広げていくことで社会貢献を行った．
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