The perturbation bound for the T-Drazin inverse of tensor and its application

Ying-Nan Cui; Hai-Feng Ma

doi:10.2298/fil2105565c

The perturbation bound for the T-Drazin inverse of tensor and its application

Filomat ◽

10.2298/fil2105565c ◽

2021 ◽

Vol 35 (5) ◽

pp. 1565-1587

Author(s):

Ying-Nan Cui ◽

Hai-Feng Ma

Keyword(s):

Drazin Inverse ◽

Tensor Equation ◽

Perturbation Bound ◽

Optimal Perturbation

In this paper, let A and B be n x n x p complex tensors and B = A + E. Denote the T-Drazin inverse of A by AD. We give a perturbation bound for ||BD-AD||=||AD|| under condition (W). Considering the solution of singular tensor equation A* x = b, (b ? R(AD)) at the same time. The optimal perturbation of T-Drazin inverse of tensors and the solution of a system of tensor equations have been given.

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An optimal perturbation bound for the partial isometry associated to the generalized polar decomposition

Applied Mathematics and Computation ◽

10.1016/j.amc.2019.124987 ◽

2020 ◽

Vol 372 ◽

pp. 124987

Author(s):

Chunhong Fu ◽

Qingxiang Xu

Keyword(s):

Polar Decomposition ◽

Partial Isometry ◽

Perturbation Bound ◽

Optimal Perturbation

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Perturbation Bound for the Drazin Inverse of the Matrix-Value Function

Advances in Mathematical Physics ◽

10.1155/2019/8136215 ◽

2019 ◽

Vol 2019 ◽

pp. 1-14

Author(s):

Yonghui Qin ◽

Zhenshu Xie ◽

Xiaoji Liu

Keyword(s):

Perturbation Analysis ◽

Upper Bound ◽

Value Function ◽

Drazin Inverse ◽

Matrix Equations ◽

Perturbation Bound ◽

The Matrix

The perturbation analysis of the differential for the Drazin inverse of the matrix-value function A(t)∈Cn×n is investigated. An upper bound of the Drazin inverse and its differential is also considered. Applications to the perturbation bound for the solution of the matrix-value function coefficients some matrix equations are given.

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An optimal perturbation bound

Mathematical Methods in the Applied Sciences ◽

10.1002/mma.5612 ◽

2019 ◽

Vol 42 (11) ◽

pp. 3791-3798

Author(s):

Youming Liu ◽

Chunguang Ren

Keyword(s):

Perturbation Bound ◽

Optimal Perturbation

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Perturbation bound of the Drazin inverse

Applied Mathematics and Computation ◽

10.1016/s0096-3003(00)00126-0 ◽

2002 ◽

Vol 125 (2-3) ◽

pp. 231-244 ◽

Cited By ~ 15

Author(s):

Yimin Wei

Keyword(s):

Drazin Inverse ◽

Perturbation Bound

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A Perturbation Bound of the Drazin Inverse of a Matrix by Separation of Simple Invariant Subspaces

SIAM Journal on Matrix Analysis and Applications ◽

10.1137/s0895479804439948 ◽

2005 ◽

Vol 27 (1) ◽

pp. 72-81 ◽

Cited By ~ 36

Author(s):

Yimin Wei ◽

Xiezhang Li ◽

Fanbin Bu

Keyword(s):

Invariant Subspaces ◽

Drazin Inverse ◽

Perturbation Bound

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A note on the perturbation bounds of W-weighted Drazin inverse of linear operator in Banach space

Filomat ◽

10.2298/fil1702505w ◽

2017 ◽

Vol 31 (2) ◽

pp. 505-511 ◽

Cited By ~ 1

Author(s):

Xue-Zhong Wang ◽

Hai-Feng Ma ◽

Marija Cvetkovic

Keyword(s):

Banach Space ◽

Linear Operator ◽

Banach Spaces ◽

Linear Operators ◽

Drazin Inverse ◽

Perturbation Bound ◽

Bounded Linear Operators ◽

Bounded Linear ◽

Perturbation Bounds ◽

Weighted Drazin Inverse

We investigate the perturbation bound of the W-weighted Drazin inverse for bounded linear operators between Banach spaces and present two explicit expressions for the W-weighted Drazin inverse of bounded linear operators in Banach space, which extend the results in Chin. Anna. Math., 21C:1 (2000) 39-44 by Wei.

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A note on the perturbation bound of the Drazin inverse

Applied Mathematics and Computation ◽

10.1016/s0096-3003(02)00230-8 ◽

2003 ◽

Vol 140 (2-3) ◽

pp. 329-340 ◽

Cited By ~ 5

Author(s):

Xiezhang Li ◽

Yimin Wei

Keyword(s):

Drazin Inverse ◽

Perturbation Bound

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Perturbation bound for the generalized Drazin inverse of an operator in Banach space

Filomat ◽

10.2298/fil1716177l ◽

2017 ◽

Vol 31 (16) ◽

pp. 5177-5191 ◽

Cited By ~ 1

Author(s):

Xiaoji Liu ◽

Yonghui Qin

Keyword(s):

Banach Space ◽

Perturbation Analysis ◽

Upper Bound ◽

Drazin Inverse ◽

Sufficient Condition ◽

Necessary And Sufficient Condition ◽

Perturbation Bound ◽

Generalized Drazin Inverse ◽

Necessary And Sufficient

In this paper, we consider perturbation analysis for the generalized Drazin inverse of an operator in Banach space. An necessary and sufficient condition for the generalized Drazin invertible is given. The upper bound is given under some certain conditions, and a relative perturbation bound is also considered.

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The Tensor Equation AX + XA = G

10.21236/ada246665 ◽

1992 ◽

Cited By ~ 1

Author(s):

Mike Scheidler

Keyword(s):

Tensor Equation

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Cline’s formula for g-Drazin inverses in a ring

Filomat ◽

10.2298/fil1908249c ◽

2019 ◽

Vol 33 (8) ◽

pp. 2249-2255

Author(s):

Huanyin Chen ◽

Marjan Abdolyousefi

Keyword(s):

Operator Theory ◽

Spectral Properties ◽

Associative Ring ◽

Linear Operators ◽

Drazin Inverse ◽

Bounded Linear Operators ◽

Bounded Linear ◽

Cline’S Formula

It is well known that for an associative ring R, if ab has g-Drazin inverse then ba has g-Drazin inverse. In this case, (ba)d = b((ab)d)2a. This formula is so-called Cline?s formula for g-Drazin inverse, which plays an elementary role in matrix and operator theory. In this paper, we generalize Cline?s formula to the wider case. In particular, as applications, we obtain new common spectral properties of bounded linear operators.

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