Development of high speed singular value decomposition algorithm for sparse matrices of large scale and upload of its source code
| Project/Area Number |
24360038
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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 |
Engineering fundamentals
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| Research Institution | Kyoto University |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
KIMURA Kinji 京都大学, 大学院情報学研究科, 特定准教授 (10447899)
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| Project Period (FY) |
2012-04-01 – 2016-03-31
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| Project Status |
Completed (Fiscal Year 2015)
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| Budget Amount *help |
¥18,850,000 (Direct Cost: ¥14,500,000、Indirect Cost: ¥4,350,000)
Fiscal Year 2014: ¥6,500,000 (Direct Cost: ¥5,000,000、Indirect Cost: ¥1,500,000)
Fiscal Year 2013: ¥5,720,000 (Direct Cost: ¥4,400,000、Indirect Cost: ¥1,320,000)
Fiscal Year 2012: ¥6,630,000 (Direct Cost: ¥5,100,000、Indirect Cost: ¥1,530,000)
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| Keywords | 特異値分解 / 大規模スパース行列 / Golub-Kahan-Lanczos法 / 部分特異対 / 再直交化 / 部分特異対計算 / ２分法 / 逆反復法 / 並列計算 / Golub-Kahan-Lanczos前処理 / 応用数学 / アルゴリズム / 固有対計算 / 固有値分解 / 実装コード公開 |
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| Outline of Final Research Achievements |
Singular value decomposition of sparse matrices of large scale is an important matrix operation which is fundamental for analyzing big data. In this research we apply the Golub-Kahan-Lanczos algorithm with reorthogonalization to sparse matrices of large scale to generate approximated tridiagonal matrices by high performance computation in parallel processing. Secondly the bisection and the inverse iteration methods are applied to them to giving a subset of eigenpairs of the originals with high reusability of data. The corresponding source codes have been uploaded one by one. When the sparse matrices are positive definite, then the resulting eigenpairs lead to a sebset of singular triplets.
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Report
(5 results)
Research Products
(45 results)
