Comprehensive development of fast numerical methods for solving large linear systems with matrix functions
Project/Area Number |
26286088
|
Research Category |
Grant-in-Aid for Scientific Research (B)
|
Allocation Type | Partial Multi-year Fund |
Section | 一般 |
Research Field |
Computational science
|
Research Institution | Nagoya University (2015-2016) Aichi Prefectural University (2014) |
Principal Investigator |
|
Co-Investigator(Kenkyū-buntansha) |
張 紹良 名古屋大学, 工学研究科, 教授 (20252273)
|
Project Period (FY) |
2014-04-01 – 2017-03-31
|
Project Status |
Completed (Fiscal Year 2016)
|
Budget Amount *help |
¥6,370,000 (Direct Cost: ¥4,900,000、Indirect Cost: ¥1,470,000)
Fiscal Year 2016: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2014: ¥3,770,000 (Direct Cost: ¥2,900,000、Indirect Cost: ¥870,000)
|
Keywords | 行列関数計算 / テンソル計算 / 線形方程式 / 行列関数 / 国際ワークショップ |
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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Report
(4 results)
Research Products
(20 results)