New developments of matrix similarity transformations derived from integrable systems
| Project/Area Number |
26400208
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Foundations of mathematics/Applied mathematics
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| Research Institution | Kyoto Prefectural University |
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Principal Investigator |
Iwasaki Masashi 京都府立大学, 生命環境科学研究科, 准教授 (30397575)
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| Co-Investigator(Renkei-kenkyūsha) |
YAMAMOTO Yusaku 電気通信大学, 大学院情報理工学研究科, 教授 (20362288)
ISHIWATA Emiko 東京理科大学, 理学部, 教授 (30287958)
KONDO Koichi 同志社大学, 理工学部, 教授 (30314397)
FUKUDA Akiko 芝浦工業大学, システム理工学部, 准教授 (70609297)
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| Research Collaborator |
SHINJO Masato
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| Project Period (FY) |
2014-04-01 – 2017-03-31
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| Project Status |
Completed (Fiscal Year 2016)
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| Budget Amount *help |
¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000)
Fiscal Year 2016: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2015: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2014: ¥2,080,000 (Direct Cost: ¥1,600,000、Indirect Cost: ¥480,000)
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| Keywords | 行列の相似変形 / dLVsアルゴリズム / 分割型ツイスト分解法 / 離散ハングリー可積分系 / 行列の帯構造 / フィボナッチ数列 / 逆固有値問題 / min-plus固有多項式 / 漸近解析 / M-行列 / Cyclic Reduction法 / MR3法 / 固有値問題 / Block cyclic reduction法 / 力学系 / 相似変形 / 行列の固有値 / 病理モデル / リーシンメトリー / Stride Reduction法 / 代数方程式 / 可積分系 / ロトカ・ボルテラ系 / Cyclic Reduction / Stride Reduction / 漸近展開 |
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| Outline of Final Research Achievements |
One of the results is to improve the I-SVD algorithm for computing singular value decompositions of bidiagonal matrices with higher accuracy. The new I-SVD algorithm employs the proposed dLVs algorithm for singular values and the proposed divided Twisted factorization method for singular vectors. The second is to investigate the convergence of solutions to dynamical systems to eigenvalues of various band matrices. Solution expressions of the discrete hungry integrable systems and their asymptotic convergence are thoroughly clarified. A new algorithm for computing eigenvalues of pentadiagonal matrices is also designed. The third is to find relationships among the discrete hungry integrable systems, extended Fibonacci sequences and roots of polynomials, and then develop them in constructing band matrices with prescribed eigenvalues. New characteristic polynomials of matrices are also presented over min-plus algebra.
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Report
(4 results)
Research Products
(23 results)
