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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.