New perturbation bounds in unitarily invariant norms for subunitary polar factors

2018 ◽  
Vol 34 ◽  
pp. 231-239
Author(s):  
Lei Zhu ◽  
Wei-wei Xu ◽  
Hao Liu ◽  
Li-juan Ma
Keyword(s):  
Polar Decomposition ◽  
Positive Semidefinite ◽  
Perturbation Bounds ◽  
Unitarily Invariant Norms ◽  
Polar Factor ◽  
New Perturbation

Let $A\in\mathbb{C}^{m \times n}$ have generalized polar decomposition $A = QH$ with $Q$ subunitary and $H$ positive semidefinite. Absolute and relative perturbation bounds are derived for the subunitary polar factor $Q$ in unitarily invariant norms and in $Q$-norms, that extend and improve existing bounds.

scholarly journals Relative and Absolute Perturbation Bounds for Weighted Polar Decomposition

2012 ◽  
Vol 2012 ◽  
pp. 1-15
Author(s):  
Pingping Zhang ◽  
Hu Yang ◽  
Hanyu Li
Keyword(s):  
Polar Decomposition ◽  
Perturbation Bounds ◽  
New Perturbation

Some new perturbation bounds for both weighted unitary polar factors and generalized nonnegative polar factors of the weighted polar decompositions are presented without the restriction thatAand its perturbed matrixA˜have the same rank. These bounds improve the corresponding recent results.

Some New Perturbation Bounds for the Generalized Polar Decomposition

2004 ◽  
Vol 44 (2) ◽  
pp. 237-244 ◽  
Author(s):  
Xiao-shan Chen ◽  
Wen Li ◽  
Weiwei Sun
Keyword(s):  
Polar Decomposition ◽  
Perturbation Bounds ◽  
New Perturbation

Some new perturbation bounds of generalized polar decomposition

2014 ◽  
Vol 233 ◽  
pp. 430-438 ◽  
Author(s):  
Xiaoli Hong ◽  
Lingsheng Meng ◽  
Bing Zheng
Keyword(s):  
Polar Decomposition ◽  
Perturbation Bounds ◽  
New Perturbation

New perturbation bounds for the subunitary polar factors

2013 ◽  
Vol 61 (4) ◽  
pp. 517-526
Author(s):  
Pingping Zhang ◽  
Hu Yang ◽  
Hanyu Li
Keyword(s):  
Perturbation Bounds ◽  
New Perturbation

Some Spectral Properties of Polar Decompositions

1984 ◽  
Vol 36 (6) ◽  
pp. 973-985
Author(s):  
Bryan E. Cain
Keyword(s):  
Polar Decomposition ◽  
Positive Semidefinite ◽  
Unitary Matrix ◽  
List Type ◽  
Complex Matrix ◽  
Important Special Case ◽  
Definition Of ◽  
Image Position ◽  
Square Complex ◽  
Special Case

The results in this paper respond to two rather natural questions about a polar decomposition A = UP, where U is a unitary matrix and P is positive semidefinite. Let λ1, …, λn be the eigenvalues of A. The questions are:(A) When will |λ1|, …, |λn| be the eigenvalues of P?(B) When will λ1/|λ1|, …, λn/|λn| be the eigenvalues of U?The complete answer to (A) is “if and only if U and P commute.” In an important special case the answer to (B) is “if and only if U2 and P commute.“Since these matters are best couched in terms of two different inertias, we begin with a unifying definition of inertia which views all inertias from a single perspective.For each square complex matrix A and each complex number z let m(A, z) denote the multiplicity of z as a root of the characteristic polynomial

New perturbation bounds for Sylvester equations

2002 ◽  
Author(s):  
N.D. Christov ◽  
S. Lesecq ◽  
M.M. Konstantinov ◽  
P.Hr. Petkov ◽  
A. Barraud
Keyword(s):  
Perturbation Bounds ◽  
New Perturbation
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