特異性をもつ線形方程式に対する反復法とその前処理
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- 保國 惠一
- 筑波大学システム情報系情報工学域
書誌事項
- タイトル別名
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- Iterative Methods and Preconditioners for Linear Systems with Singularity
説明
<p>Linear systems involving singularity arise in a wide range of applications throughout computational science and engineering. This article aims at presenting and discussing iterative methods for solving linear systems with singularity, with an emphasis on stationary (matrix splitting) and Krylov subspace iterative methods and preconditioning techniques. For singular matrices, conventional preconditioners based on incomplete matrix factorizations may break down, whereas particular stationary iterative methods combined with Krylov subspace methods may avoid breakdown. Although classical stationary iterative methods have been regarded as slow to converge, recent stationary iterative methods have convergence speed competitive with Krylov subspace methods, and may dramatically improve the convergence of Krylov subspace methods when applied as preconditioners. We present recent results on their convergence theories in general and for particular problems such as saddle point systems and least squares problems.</p>
収録刊行物
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- 応用数理
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応用数理 28 (2), 11-18, 2018-06-26
一般社団法人 日本応用数理学会
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詳細情報 詳細情報について
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- CRID
- 1390845713004318976
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- NII論文ID
- 130007492195
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- ISSN
- 24321982
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- 本文言語コード
- ja
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- データソース種別
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- JaLC
- CiNii Articles
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- 抄録ライセンスフラグ
- 使用不可