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Numerical Unstability and Improvement of a No-Pivoting LU Decomposition Algorithm by a Discrete Fourier Matrix
https://ipsj.ixsq.nii.ac.jp/records/158496
https://ipsj.ixsq.nii.ac.jp/records/158496e725fccf-09fd-4d0e-90e5-241c6f6e2e40
| 名前 / ファイル | ライセンス | アクション |
|---|---|---|
IPSJ-HPC16154006.pdf (1.1 MB)
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Copyright (c) 2016 by the Information Processing Society of Japan
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| オープンアクセス | ||
| Item type | SIG Technical Reports(1) | |||||||
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| 公開日 | 2016-04-18 | |||||||
| タイトル | ||||||||
| タイトル | Numerical Unstability and Improvement of a No-Pivoting LU Decomposition Algorithm by a Discrete Fourier Matrix | |||||||
| タイトル | ||||||||
| 言語 | en | |||||||
| タイトル | Numerical Unstability and Improvement of a No-Pivoting LU Decomposition Algorithm by a Discrete Fourier Matrix | |||||||
| 言語 | ||||||||
| 言語 | eng | |||||||
| キーワード | ||||||||
| 主題Scheme | Other | |||||||
| 主題 | 行列計算 | |||||||
| 資源タイプ | ||||||||
| 資源タイプ識別子 | http://purl.org/coar/resource_type/c_18gh | |||||||
| 資源タイプ | technical report | |||||||
| 著者所属 | ||||||||
| Department of Computer Science, The University of Tokyo | ||||||||
| 著者所属(英) | ||||||||
| en | ||||||||
| Department of Computer Science, The University of Tokyo | ||||||||
| 著者名 |
Shohei, Kobayashi
× Shohei, Kobayashi
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| 著者名(英) |
Shohei, Kobayashi
× Shohei, Kobayashi
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| 論文抄録 | ||||||||
| 内容記述タイプ | Other | |||||||
| 内容記述 | Linear systems are solved by LU decomposition. Partial pivoting is the most frequently employed way to perform this decomposition. Pivoting is necessary for numerical stability of LU decomposition. However, pivoting is not able to be computed in parallel and pivoting restricts block LU decomposition algorithms. A no-pivoting LU decomposition algorithm has been investigated for more than two decades. This decomposition algorithm without pivoting is efficient for modern computers. However, stabilizing numerical accuracy of solutions of linear systems without pivoting is more difficult than partial pivoting. This thesis researches the algorithm called RDFT that eliminates pivoting nessesity by using random numbers and discrete Fourier transform. We show some examples of LU decomposition by RDFT fail numerically. In addition, we improve the RDFT algorithm with modification to improve numerical stability of such matrices. | |||||||
| 論文抄録(英) | ||||||||
| 内容記述タイプ | Other | |||||||
| 内容記述 | Linear systems are solved by LU decomposition. Partial pivoting is the most frequently employed way to perform this decomposition. Pivoting is necessary for numerical stability of LU decomposition. However, pivoting is not able to be computed in parallel and pivoting restricts block LU decomposition algorithms. A no-pivoting LU decomposition algorithm has been investigated for more than two decades. This decomposition algorithm without pivoting is efficient for modern computers. However, stabilizing numerical accuracy of solutions of linear systems without pivoting is more difficult than partial pivoting. This thesis researches the algorithm called RDFT that eliminates pivoting nessesity by using random numbers and discrete Fourier transform. We show some examples of LU decomposition by RDFT fail numerically. In addition, we improve the RDFT algorithm with modification to improve numerical stability of such matrices. | |||||||
| 書誌レコードID | ||||||||
| 収録物識別子タイプ | NCID | |||||||
| 収録物識別子 | AN10463942 | |||||||
| 書誌情報 |
研究報告ハイパフォーマンスコンピューティング（HPC） 巻 2016-HPC-154, 号 6, p. 1-8, 発行日 2016-04-18 |
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| ISSN | ||||||||
| 収録物識別子タイプ | ISSN | |||||||
| 収録物識別子 | 2188-8841 | |||||||
| Notice | ||||||||
| SIG Technical Reports are nonrefereed and hence may later appear in any journals, conferences, symposia, etc. | ||||||||
| 出版者 | ||||||||
| 言語 | ja | |||||||
| 出版者 | 情報処理学会 | |||||||
