Jacobi-Davidson methods for cubic eigenvalue problems

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

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

39 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)605-624
Number of pages20
JournalNumerical Linear Algebra with Applications
Issue number7
Publication statusPublished - 2005 Sept


  • 3D schrödinger equation
  • Cubic Jacobi-Davidson method
  • Cubic eigenvalue problem
  • Non-equivalence deflation

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Applied Mathematics


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