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Behavior of the Correction Equations in the Jacobi–Davidson Method

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  • Yuan Kong
  • Yong Fang

Abstract

The Jacobi–Davidson iteration method is efficient for computing several eigenpairs of Hermitian matrices. Although the involved correction equation in the Jacobi–Davidson method has many developed variants, the behaviors of them are not clear for us. In this paper, we aim to explore, theoretically, the convergence property of the Jacobi–Davidson method influenced by different types of correction equations. As a by-product, we derive the optimal expansion vector, which imposed a shift-and-invert transform on a vector located in the prescribed subspace, to expand the current subspace.

Suggested Citation

  • Yuan Kong & Yong Fang, 2019. "Behavior of the Correction Equations in the Jacobi–Davidson Method," Mathematical Problems in Engineering, Hindawi, vol. 2019, pages 1-4, August.
    • Handle: RePEc:hin:jnlmpe:5169362
    DOI: 10.1155/2019/5169362
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