2018 Fiscal Year Final Research Report
Development of accurate algorithms for numerical linear algebra
| Project/Area Number |
16H03917
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Computational science
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| Research Institution | Tokyo Woman's Christian University |
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Principal Investigator |
Ogita Takeshi 東京女子大学, 現代教養学部, 教授 (00339615)
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| Co-Investigator(Kenkyū-buntansha) |
尾崎 克久 芝浦工業大学, システム理工学部, 准教授 (90434282)
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| Project Period (FY) |
2016-04-01 – 2019-03-31
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| Keywords | 高精度数値線形代数 |
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| Outline of Final Research Achievements |
For linear systems, we conducted on numerical algorithms that can always obtain the best approximate solution regardless of the condition number of the coefficient matrix.
We developed an iterative improvement algorithm for eigenvectors with quadratic convergence for symmetric eigenvalue problems. This enables us to develop a numerical algorithm that can always obtain the best approximate solution. We also developed a numerical algorithm that can always obtain the best approximate solution of singular value problems for nonsymmetric matrices.
In order to improve the efficiency of the above proposed algorithms, we developed accurate matrix multiplication algorithms. In addition, as test problems in numerical linear algebra, we developed methods for generating problems with exact solutions.
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| Free Research Field |
精度保証付き数値計算
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| Academic Significance and Societal Importance of the Research Achievements |
科学技術計算では、理工学の様々な分野において多くの問題を数値線形代数の問題に帰着する。本研究では、そのような問題において、常に最良の近似解を得ることが可能な数値計算アルゴリズムについて研究を実施した。これは、数値線形代数をはじめとして数値計算の新たな方向性を開拓するものであり、本研究の遂行が計算科学の分野に与える学術的な意義は極めて大きい。そして、すべての科学技術計算における品質及び信頼性の向上に貢献する研究であるため、実用上も非常に有用である。
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