z-logo
Premium
An optimal perturbation bound
Author(s) -
Liu Youming,
Ren Chunguang
Publication year - 2019
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5612
Subject(s) - mathematics , linear subspace , perturbation (astronomy) , zhàng , singular perturbation , norm (philosophy) , singular value , annals , invariant (physics) , pure mathematics , mathematical analysis , mathematical physics , law , eigenvalues and eigenvectors , physics , quantum mechanics , political science , china , ancient history , history
Cai and Zhang establish separate perturbation bounds for sin Θ distances with spectral and Frobenius norms (Cai T, Zhang A. Rate‐optimal perturbation bounds for singular subspaces with applications to high‐dimensional statistics. The Annals of Statistics. 2018; Vol. 46, No. 1: 60−89). We extend their theorem to each unitarily invariant norm. It turns out that our estimation is optimal as well.

This content is not available in your region!

Continue researching here.

Having issues? You can contact us here