A Note on Perturbation Estimations for Spectral Projectors. (25th October 2020)

• Record Type: Journal Article
• Authors: Song, Chuanning; Wei, Yimin; Xu, Qingxiang
• Is Part Of: Numerical functional analysis and optimization. Volume 41:Number 14(2020)
• Page Start: 1741
• Page End: 1747
• Publication Date: 2020-10-25
• Subjects: Drazin inverse -- spectral projector -- stable perturbation; 15A09 -- 65F20; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2020.1813161
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: For any singular matrix A ∈ C n × n, let A D, A π = I n − A A D be its Drazin inverse and spectral projector, respectively. Let | | · | | be any norm on C n × n and A ¯ ∈ C n × n be any stable perturbation of A . In this note a sufficient condition is given under which | | A ¯ π − A π | | < 1 .