On multistep Rayleigh quotient iterations for Hermitian eigenvalue problems. (1st May 2019)

• Record Type: Journal Article
• Authors: Bai, Zhong-Zhi; Miao, Cun-Qiang; Jian, Shuai
• Is Part Of: Computers & mathematics with applications. Volume 77:issue 9(2019)
• Page Start: 2396
• Page End: 2406
• Publication Date: 2019-05-01
• Subjects: Hermitian eigenvalue problem -- Rayleigh quotient iteration -- Multistep modification -- Inexact solve -- Preconditioning; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2018.12.025
• Languages: English
• ISSNs: 0898-1221

Abstract

Abstract: We present a multistep Rayleigh quotient iteration, as well as its inexact variant, for computing an eigenpair of a large sparse Hermitian matrix. Theoretical analysis shows that both exact and inexact multistep Rayleigh quotient iterations converge much faster than the exact and inexact Rayleigh quotient iterations, respectively. For the inexact multistep Rayleigh quotient iteration, we use the preconditioned conjugate gradient method to solve the inner linear systems, and find that significant saving in the number of inner iteration steps can be achieved when choosing a proper preconditioner. Numerical examples demonstrate effectiveness and superiority of our methods.