Behavior of the Correction Equations in the Jacobi–Davidson Method. (5th August 2019)

• Record Type: Journal Article
• Authors: Kong, Yuan; Fang, Yong
• Other Names: Vipiana Francesca Academic Editor.
• Is Part Of: Mathematical problems in engineering. Volume 2019(2019)
• Publication Date: 2019-08-05
• Subjects: Engineering mathematics -- Periodicals; 510.2462
• DOI: 10.1155/2019/5169362
• Languages: English
• ISSNs: 1024-123X

Abstract

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.