A note on convergence and a posteriori error estimates of the classical Jacobi method
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- Tsuchiya Takuya
- Graduate School of Science and Engineering, Ehime University
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- Aishima Kensuke
- Department of Mathematical Informatics, Graduate School of Information Science and Technology, The University of Tokyo
書誌事項
- タイトル別名
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- A note on convergence and <i>a posteriori</i> error estimates of the classical Jacobi method
抄録
We consider convergence and a posteriori error estimates of the classical Jacobi method for solving symmetric eigenvalue problems. The famous convergence proof of the classical Jacobi method consists of two phases. First, it is shown that all the off-diagonal elements converge to zero. Then, from a perturbation theorem, Parlett or Wilkinson shows convergence of the diagonal elements in the textbooks. Ciarlet also gives another convergence proof based on a discussion about a bounded sequence corresponding to a diagonal element. In this paper, we simplify the Ciarlet's convergence proof. Our proof does not use any perturbation theory. Moreover, employing this approach, we obtain a posteriori error estimates for eigenvectors.
収録刊行物
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- Nonlinear Theory and Its Applications, IEICE
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Nonlinear Theory and Its Applications, IEICE 6 (3), 391-396, 2015
一般社団法人 電子情報通信学会
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詳細情報 詳細情報について
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- CRID
- 1390001205345474560
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- NII論文ID
- 130005085580
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- ISSN
- 21854106
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- 本文言語コード
- en
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- データソース種別
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- JaLC
- Crossref
- CiNii Articles
- KAKEN
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- 抄録ライセンスフラグ
- 使用不可