Combined perturbation bounds : II. Polar decompositions
Research output: Journal Publications and Reviews (RGC: 21, 22, 62) › 22_Publication in policy or professional journal
Author(s)
Related Research Unit(s)
Detail(s)
| Original language | English |
|---|---|
| Pages (from-to) | 1339-1346 |
| Journal / Publication | Science in China, Series A: Mathematics |
| Volume | 50 |
| Issue number | 9 |
| Publication status | Published - Sept 2007 |
Link(s)
Abstract
In this paper, we study the perturbation bounds for the polar decomposition A = QH where Q is unitary and H is Hermitian. The optimal (asymptotic) bounds obtained in previous works for the unitary factor, the Hermitian factor and singular values of A are σ r 2 ΔQ F 2 Δ F 2 , 1/2ΔH F 2 ΔA F 2 and Δ∑ F 2 ΔA F 2 , respectively, where ∑ = diag(σ 1, σ 2, σ r , 0 ) is the singular value matrix of A and σ r denotes the smallest nonzero singular value. Here we present some new combined (asymptotic) perturbation bounds σ r 2 ΔQ F 2 +1/2 ΔH F 2 ΔA F 2 and σ r 2 Delta;Q F 2 + Δ∑ F 2 ΔA F 2 which are optimal for each factor. Some corresponding absolute perturbation bounds are also given. © 2007 Science in China Press.
Research Area(s)
- Perturbation, Polar decomposition, Singular value
Citation Format(s)
Combined perturbation bounds: II. Polar decompositions. / Li, Wen; Sun, Wei-Wei.
In: Science in China, Series A: Mathematics, Vol. 50, No. 9, 09.2007, p. 1339-1346.
In: Science in China, Series A: Mathematics, Vol. 50, No. 9, 09.2007, p. 1339-1346.
Research output: Journal Publications and Reviews (RGC: 21, 22, 62) › 22_Publication in policy or professional journal
