2012 Fiscal Year Final Research Report
Studies on matrix diagonalization by solving nonlinear systems
| Project/Area Number |
21740086
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Doshisha University |
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Principal Investigator |
KONDO Koichi 同志社大学, 理工学部, 准教授 (30314397)
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| Project Period (FY) |
2009 – 2012
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| Keywords | 固有値分解 / 特異値分解 / 非線形解析 / ニュートン法 / 数値計算アルゴリズム |
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| Research Abstract |
The matrix diagonalizations, for example eigenvalue decomposition, singular value decomposition, are basic topics in linear algebra, and they also important tools in various fields. In this research, we developed new method, which is called the hyperplane-constrained method. This method can obtain matrix diagonalization by solving the nonlinear systems, which are constrained on hyperplanes, by the Newton method. The problems on selecting initial vectors of the Newton method is avoided by suitable selecting the normal vectors of the hyperplanes.
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