Rank-one perturbation bounds for singular values of arbitrary matrices

Journal of Inequalities and Applications

Hao Liu¹  Lei Zhu²  Xiaofei Peng³ 

[1] 0000 0000 9558 9911, grid.64938.30, College of Science, Nanjing University of Aeronautics and Astronautics, Nanjing, P.R. China;0000 0000 9750 7019, grid.27871.3b, College of Engineering, Nanjing Agricultural University, Nanjing, P.R. China;0000 0004 0368 7397, grid.263785.d, School of Mathematical Sciences, South China Normal University, Guangzhou, P.R. China;

关键词: Arbitrary matrix;    Singular values;    Eigenvalue gap;    Rank-one update;    65F15;    65H10;    65H20;   

DOI  :  10.1186/s13660-019-2089-4

来源: publisher

【 摘 要 】

Rank-one perturbation of arbitrary matrices has many practical applications. In this paper, based on the relationship between the singular values and the eigenvalues, we discuss singular value variations and present two-side bounds of the singular values for rank-one perturbation of arbitrary matrices. Numerical results confirm that the proposed perturbation bounds are sharper than some existing bounds.

【 授权许可】

CC BY