Relative perturbation bounds for the unitary polar factor

1997 ◽  
Vol 37 (1) ◽  
pp. 67-75 ◽  
Author(s):  
Ren-Cang Li
Keyword(s):  
Perturbation Bounds ◽  
Polar Factor

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 Applications of Paz's inequality to perturbation bounds for Markov chains

1998 ◽  
Vol 268 ◽  
pp. 183-196 ◽  
Author(s):  
Stephen J. Kirkland ◽  
Michael Neumann ◽  
Bryan L. Shader
Keyword(s):  
Markov Chains ◽  
Perturbation Bounds

Perturbation Bounds and Condition Numbers for a Complex Indefinite Linear Algebraic System

2016 ◽  
Vol 6 (2) ◽  
pp. 211-221 ◽  
Author(s):  
Lei Zhu ◽  
Wei-Wei Xu ◽  
Xing-Dong Yang
Keyword(s):  
Algebraic System ◽  
Condition Numbers ◽  
Linear Algebraic System ◽  
Science And Engineering ◽  
Numerical Examples ◽  
Interest In Science ◽  
Perturbation Bounds

AbstractWe consider perturbation bounds and condition numbers for a complex indefinite linear algebraic system, which is of interest in science and engineering. Some existing results are improved, and illustrative numerical examples are provided.

scholarly journals The minimization of matrix logarithms: On a fundamental property of the unitary polar factor

2014 ◽  
Vol 449 ◽  
pp. 28-42 ◽  
Author(s):  
Johannes Lankeit ◽  
Patrizio Neff ◽  
Yuji Nakatsukasa
Keyword(s):  
Fundamental Property ◽  
Polar Factor
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