A note on convergence and a posteriori error estimates of the classical Jacobi method

• Tsuchiya Takuya

  Graduate School of Science and Engineering, Ehime University

• 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

• 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

• Nonlinear Theory and Its Applications, IEICE

  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

キーワード

• eigenvalues
• classical Jacobi method
• error estimations

詳細情報

• CRID: 1390001205345474560
• NII論文ID: 130005085580
• DOI: 10.1587/nolta.6.391
• ISSN: 21854106
• Web Site: https://www.jstage.jst.go.jp/article/nolta/6/3/6_391/_pdf
• 本文言語コード: en
• データソース種別:
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• 抄録ライセンスフラグ: 使用不可