| Project/Area Number |
24740110
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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 |
Global analysis
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| Research Institution | Shibaura Institute of Technology (2014)
Tokyo University of Science (2012-2013) |
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Principal Investigator |
FUKUDA Akiko 芝浦工業大学, システム理工学部, 助教 (70609297)
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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 |
¥3,380,000 (Direct Cost: ¥2,600,000、Indirect Cost: ¥780,000)
Fiscal Year 2014: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2013: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2012: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
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| Keywords | 離散可積分系 / 固有値 / 離散戸田方程式 / 超離散化 / 保存量 / 中心多様体 / 収束次数 / 原点シフト / 離散ハングリー戸田方程式 / totally nonnegative行列 / 離散ハングリーロトカ・ボルテラ系 / Newtonシフト / 可積分系 / 箱玉系 / Totally Nonnegative行列 / dqdsアルゴリズム / 中心多様体理論 / 誤差解析 |
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| Outline of Final Research Achievements |
In the previous study, we have designed two algorithms: the dhLV algorithm for computing eigenvalues of nonsymmetric banded matrix based on the discrete hungry Lotka-Volterra (dhLV) system, and the dhToda algorithm for computing eigenvalues of totally nonnegative matrix based on the discrete hungry Toda (dhToda) equation.
In this study, for these algorithms, we incorporate the technique for faster convergence, and clarify rounding errors, global convergence, local convergence and convergence rate. It is also clarified that the eigenvectors can be computed efficiently.
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