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NII Technical Report (NII-2001-002E)：On the Behaviour of the Conjugate Residual Method for Singular Systems
https://doi.org/10.20736/0000000354
https://doi.org/10.20736/0000000354ac21fc4a-91a2-458c-9fbf-5b1aa3e08e2e
| 名前 / ファイル | ライセンス | アクション |
|---|---|---|
NII Technical Report (NII-2001-002E)：On the Behaviour of the Conjugate Residual Method for Singular Systems (163.3 kB)
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| アイテムタイプ | レポート / Report(1) | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| 公開日 | 2001-07-04 | |||||||||
| タイトル | ||||||||||
| タイトル | NII Technical Report (NII-2001-002E)：On the Behaviour of the Conjugate Residual Method for Singular Systems | |||||||||
| 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 | 10.20736/0000000354 | |||||||||
| ID登録タイプ | JaLC | |||||||||
| 著者 |
速水, 謙
× 速水, 謙
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| 抄録 | ||||||||||
| 内容記述タイプ | Abstract | |||||||||
| 内容記述 | Consider applying the Conjugate Residual (CR) method, which is a Krylov subspace type iterative solver, to systems of linear equations $ A {\bf x} = {\bf b} $ or least squares problems $ {\displaystyle \min_{ {\bf x} \in \rn} \| {\bf b} - A {\bf x} \|_2 } $, where $ A $ is singular and nonsymmetric. We will show that when $R(A)^\perp=\ker A$, the CR method can be decomposed into the $ R(A) $ and $ \ker A $ components, and the necessary and sufficient condition for the CR method to converge to the least squares solution without breaking down for arbitrary $ {\bf b} $ and initial approximate solution $ {\bf x}_0, $ is that the symmetric part $ M(A) $ of $ A $ is semi-definite and $ \rank \, M(A) = \rank A $. Furthermore, when ${\bf x}_0 \in R(A), $ the approximate solution converges to the pseudo inverse solution. Next, we will also derive the necessary and sufficient condition for the CR method to converge to the least squares solution without breaking down for arbitrary initial approximate solutions, for the case when $ R(A) \oplus \ker A = \rn $ and $ {\bf b} \in R(A). $ | |||||||||
| 言語 | en | |||||||||
| 書誌情報 |
ja : NIIテクニカル・レポート en : NII Technical Report 発行日 2001-07-04 |
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| 出版者 | ||||||||||
| 出版者 | 国立情報学研究所 | |||||||||
| 言語 | ja | |||||||||
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| 収録物識別子タイプ | ISSN | |||||||||
| 収録物識別子 | 1346-5597 | |||||||||
