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NII Technical Report (NII-2020-004E):GMRES on singular systems revisited
https://doi.org/10.20736/0002000372
https://doi.org/10.20736/000200037259caceeb-75e9-4f65-886a-9dda3e0aba4a
名前 / ファイル | ライセンス | アクション |
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NII Technical Report (NII-2020-004E):GMRES on singular systems revisited (139 KB)
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Item type | レポート / Report(1) | |||||||||||||
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公開日 | 2022-06-09 | |||||||||||||
タイトル | ||||||||||||||
言語 | en | |||||||||||||
タイトル | NII Technical Report (NII-2020-004E):GMRES on singular systems revisited | |||||||||||||
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 | 10.20736/0002000372 | |||||||||||||
ID登録タイプ | JaLC | |||||||||||||
著者 |
速水, 謙
× 速水, 謙
× 杉原, 光太
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抄録 | ||||||||||||||
内容記述タイプ | Abstract | |||||||||||||
内容記述 | In [Hayami K, Sugihara M. Numer Linear Algebra Appl. 2011; 18:449--469], the authors analyzed the convergence behaviour of the Generalized Minimal Residual (GMRES) method for the least squares problem $ \min_{x \in R^n} {\| b - A x \|_2}^2$, where $ A \in R^{nxn}$ may be singular and $ b \in R^n, by decomposing the algorithm into the range $ R(A) $ and its orthogonal complement $ R(A)^\perp $ components. However, we found that the proof of the fact that GMRES gives a least squares solution if $ R(A) = R(A^T) $ was not complete. In this paper, we will give a complete proof. | |||||||||||||
言語 | en | |||||||||||||
書誌情報 |
ja : NIIテクニカル・レポート en : NII Technical Report p. 1-13, 発行日 2020-09-10 |
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出版者 | ||||||||||||||
言語 | ja | |||||||||||||
出版者 | 国立情報学研究所 | |||||||||||||
ISSN | ||||||||||||||
収録物識別子タイプ | ISSN | |||||||||||||
収録物識別子 | 1346-5597 |