scholarly journals Multiplicative perturbation bounds for weighted unitary polar factor

2010 ◽  
pp. 537-554
Author(s):  
Hu Yang ◽  
Hanyu Li ◽  
Hua Shao
Keyword(s):  
Perturbation Bounds ◽  
Polar Factor ◽  
Multiplicative Perturbation

Multiplicative perturbation bounds for weighted polar decomposition

CALCOLO ◽  
2013 ◽  
Vol 51 (4) ◽  
pp. 515-529 ◽  
Author(s):  
Xiaoli Hong ◽  
Lingsheng Meng ◽  
Bing Zheng
Keyword(s):  
Polar Decomposition ◽  
Perturbation Bounds ◽  
Multiplicative Perturbation

scholarly journals Multiplicative perturbation bounds of the group inverse and oblique projection

Filomat ◽  
2016 ◽  
Vol 30 (12) ◽  
pp. 3171-3175 ◽  
Author(s):  
Lingsheng Meng ◽  
Bing Zheng
Keyword(s):  
Unitarily Invariant Norm ◽  
Group Inverse ◽  
Oblique Projection ◽  
Perturbation Bounds ◽  
Invariant Norm ◽  
Multiplicative Perturbation

In this paper, the multiplicative perturbation bounds of the group inverse and related oblique projection under general unitarily invariant norm are presented by using the decompositions of B# - A# and BB# - AA#.

scholarly journals Perturbation analysis for the Takagi vector matrix

2021 ◽  
Vol 10 (1) ◽  
pp. 23-33
Author(s):  
Aamir Farooq ◽  
Mahvish Samar ◽  
Rewayat Khan ◽  
Hanyu Li ◽  
Muhammad Kamran
Keyword(s):  
Perturbation Analysis ◽  
Original Matrix ◽  
Numerical Examples ◽  
Perturbation Bounds ◽  
Multiplicative Perturbation ◽  
Vector Matrix

Abstract In this article, we present some perturbation bounds for the Takagi vector matrix when the original matrix undergoes the additive or multiplicative perturbation. Two numerical examples are given to illuminate these bounds.

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.

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