Jacobi-Davidson methods for cubic eigenvalue problems

Tsung Min Hwang, Wen Wei Lin, Jinn Liang Liu, Weichung Wang

研究成果: 雜誌貢獻文章同行評審

37 引文 斯高帕斯(Scopus)

摘要

Several Jacobi-Davidson type methods are proposed for computing interior eigenpairs of large-scale cubic eigenvalue problems. To successively compute the eigenpairs, a novel explicit non-equivalence deflation method with low-rank updates is developed and analysed. Various techniques such as locking, search direction transformation, restarting, and preconditioning are incorporated into the methods to improve stability and efficiency. A semiconductor quantum dot model is given as an example to illustrate the cubic nature of the eigenvalue system resulting from the finite difference approximation. Numerical results of this model are given to demonstrate the convergence and effectiveness of the methods. Comparison results are also provided to indicate advantages and disadvantages among the various methods.

原文英語
頁(從 - 到)605-624
頁數20
期刊Numerical Linear Algebra with Applications
12
發行號7
DOIs
出版狀態已發佈 - 2005 九月

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Applied Mathematics

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