On the convergence of Ritz pairs and refined Ritz vectors for quadratic eigenvalue problems

Tsung Ming Huang, Zhongxiao Jia, Wen Wei Lin

研究成果: 雜誌貢獻期刊論文同行評審

4 引文 斯高帕斯(Scopus)

摘要

For a given subspace, the Rayleigh-Ritz method projects the large quadratic eigenvalue problem (QEP) onto it and produces a small sized dense QEP. Similar to the Rayleigh-Ritz method for the linear eigenvalue problem, the Rayleigh-Ritz method defines the Ritz values and the Ritz vectors of the QEP with respect to the projection subspace. We analyze the convergence of the method when the angle between the subspace and the desired eigenvector converges to zero. We prove that there is a Ritz value that converges to the desired eigenvalue unconditionally but the Ritz vector converges conditionally and may fail to converge. To remedy the drawback of possible non-convergence of the Ritz vector, we propose a refined Ritz vector that is mathematically different from the Ritz vector and is proved to converge unconditionally. We construct examples to illustrate our theory.

原文英語
頁(從 - 到)941-958
頁數18
期刊BIT Numerical Mathematics
53
發行號4
DOIs
出版狀態已發佈 - 2013 十二月

ASJC Scopus subject areas

  • Software
  • Computer Networks and Communications
  • Computational Mathematics
  • Applied Mathematics

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