2016 Fiscal Year Final Research Report
Comprehensive development of fast numerical methods for solving large linear systems with matrix functions
| Project/Area Number |
26286088
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Partial Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Computational science
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| Research Institution | Nagoya University (2015-2016)
Aichi Prefectural University (2014) |
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Principal Investigator |
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| Project Period (FY) |
2014-04-01 – 2017-03-31
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| Keywords | 行列関数計算 / テンソル計算 / 線形方程式 |
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| Outline of Final Research Achievements |
The purpose of the research project is to develop fast numerical algorithms for solving linear systems with matrix functions, and the research project mainly yielded the following results: (1) an efficient Krylov subspace method for solving linear systems with some matrix polynomials; (2) a method for boosting the speed of convergence of Newton's iterations to compute the matrix principal square root; (3) a cost-efficient variant of Incremental Newton method for the matrix principal pth root; (4) tensor decomposition algorithms for some special matrices. The results (2),(3) may lead to efficient Krylov solvers for the corresponding linear systems. The result (4) yields a novel direction for the case where the coefficient matrix has a tensor structure, which was not expected before the research project.
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| Free Research Field |
数値線形代数
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