WEKO3
アイテム
NII Technical Report (NII-2009-007E)：A Geometric View of Krylov Subspace Methods on Singular Systems
https://doi.org/10.20736/0000001253
https://doi.org/10.20736/0000001253adc0ea68-cbcf-46bd-bfba-7b2ded12cf1b
| 名前 / ファイル | ライセンス | アクション |
|---|---|---|
NII Technical Report (NII-2009-007E)：A Geometric View of Krylov Subspace Methods on Singular Systems (347.1 kB)
|
|
| Item type | レポート / Report(1) | |||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 公開日 | 2019-03-12 | |||||||||||||
| タイトル | ||||||||||||||
| タイトル | NII Technical Report (NII-2009-007E)：A Geometric View of Krylov Subspace Methods on 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 | 10.20736/0000001253 | |||||||||||||
| ID登録タイプ | JaLC | |||||||||||||
| 著者 |
速水, 謙
× 速水, 謙
× 杉原, 正顯
|
|||||||||||||
| 抄録 | ||||||||||||||
| 内容記述タイプ | Abstract | |||||||||||||
| 内容記述 | Consider applying Krylov subspace methods to systems of linear equations Ax=b or least squares problems min||b-Ax||, where A may be singular and/or nonsymmetric. Let R(A) and N(A) be the range and null space of A, respectively. Brown and Walker gave some conditions concerning R(A) and N(A) for the Generalized Minimal Residual (GMRES) method to converge to a least squares solution without breakdown for singular systems. In this paper, we provide a geometrical view of Krylov subspace methods applied to singular systems by decomposing the algorithm into components of R(A) and its orthogonal complement. Taking coordinates along R(A) and its orthogonal complement will provide an interpretation of the conditions given in Brown and Walker, at the same time giving new proofs for the conditions. We will apply the approach to the GMRES and GMRES(k) methods as well as the Generalized Conjugate Residual (GCR(k)) method, deriving conditions for convergence for inconsistent and consistent singular systems, for each method. Finally, we give examples arising in the finite difference discretization of two-point boundary value problems of an ordinary differential equation as an illustration of the convergence conditions. |
|||||||||||||
| 言語 | en | |||||||||||||
| 書誌情報 |
ja : NIIテクニカル・レポート en : NII Technical Report p. 1-28, 発行日 2009-03-26 |
|||||||||||||
| 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 | |||||||||||||
