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NII Technical Report (NII-2004-006E)：Preconditioned GMRES Methods for Least Squares Problems
https://doi.org/10.20736/0000000394
https://doi.org/10.20736/00000003940200daae-93f2-4dad-bf84-b2f2f1b1d4eb
| 名前 / ファイル | ライセンス | アクション |
|---|---|---|
NII Technical Report (NII-2004-006E)：Preconditioned GMRES Methods for Least Squares Problems (363.7 kB)
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| Item type | レポート / Report(1) | |||||||||||||
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| 公開日 | 2004-05-07 | |||||||||||||
| タイトル | ||||||||||||||
| タイトル | NII Technical Report (NII-2004-006E)：Preconditioned GMRES Methods for Least Squares Problems | |||||||||||||
| 言語 | en | |||||||||||||
| 言語 | ||||||||||||||
| 言語 | eng | |||||||||||||
| キーワード | ||||||||||||||
| 言語 | ja | |||||||||||||
| 主題Scheme | Other | |||||||||||||
| 主題 | テクニカルレポート | |||||||||||||
| キーワード | ||||||||||||||
| 言語 | en | |||||||||||||
| 主題Scheme | Other | |||||||||||||
| 主題 | Technical Report | |||||||||||||
| 資源タイプ | ||||||||||||||
| 資源 | http://purl.org/coar/resource_type/c_6501 | |||||||||||||
| タイプ | departmental bulletin paper | |||||||||||||
| ID登録 | ||||||||||||||
| ID登録 | 10.20736/0000000394 | |||||||||||||
| ID登録タイプ | JaLC | |||||||||||||
| 著者 |
伊藤, 徳史
× 伊藤, 徳史
× 速水, 謙
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| 抄録 | ||||||||||||||
| 内容記述タイプ | Abstract | |||||||||||||
| 内容記述 | For least squares problems of minimizing || b - A x ||_2 where A is a large sparse m x n (m >= n) matrix, the common method is to apply the conjugate gradient method to the normal equation A^T A x = A^T b. However, the condition number of A^T A is square of that of A, and convergence becomes problematic for severely ill-conditioned problems even with preconditioning. In this paper, we propose two methods for applying the GMRES method to the least squares problem by using a n x m matrix B. We give the necessary and sufficient condition that B should satisfy in order that the proposed methods give a least squares solution. Then, for implementations for B, we propose an incomplete QR decomposition IMGS(l). Numerical experiments show that the simplest case l=0, which is equivalent to B= ( diag (A^T A) )^(-1) A^T, gives best results, and converges faster than previous methods for severely ill-conditioned problems. | |||||||||||||
| 言語 | en | |||||||||||||
| 書誌情報 |
ja : NIIテクニカル・レポート en : NII Technical Report p. 1-29, 発行日 2004-05-07 |
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| 出版者 | ||||||||||||||
| 出版者 | 国立情報学研究所 | |||||||||||||
| 言語 | ja | |||||||||||||
| ISSN | ||||||||||||||
| 収録物識別子タイプ | ISSN | |||||||||||||
| 収録物識別子 | 1346-5597 | |||||||||||||
