2010 Fiscal Year Final Research Report
Development and Application of Multiple Division Divide-and-Conquer Algorithm for Real Symmetric Eigenproblem
| Project/Area Number |
19560058
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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 | Saitama University |
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Principal Investigator |
SHIGEHARA Takaomi Saitama University, 大学院・理工学研究科, 教授 (60206084)
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| Research Collaborator |
HIRAOKA Kazuyuki 和歌山工業高等専門学校, 一般科目, 准教授 (00312918)
HASHIGUCHI Hiroki 埼玉大学, 大学院・理工学研究科, 准教授 (50266920)
KUWAJIMA Yutaka 埼玉大学, 大学院・理工学研究科, 助教 (40451736)
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| Project Period (FY) |
2007 – 2010
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| Keywords | 数理工学 / アルゴリズム / 実対称固有値問題 / 特異値分解 / 分割統治法 / ジョルダン標準形 / クロネッカ標準形 / 並列化 |
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| Research Abstract |
Numerical linear algebra plays an important role in a large scale numerical simulation in various scientific and technological fields. It is because the core process of the simulation programs are often composed of matrix computations such as linear equation, eigenproblem and singular value decomposition. In this research, we proposed some methods to improve the multiple division divide-and-conquer algorithm for real symmetric eigenproblem, which has been recently proposed by our group. As an application, we established the multiple division divide-and-conquer algorithm for singular value decomposition. Furthermore, we proposed new efficient algorithms to compute Jordan canonical form for square matrices and Kronecker canonical form for matrix pencils.
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