Results 171 to 180 of about 640 (203)

The perturbation of the Drazin inverse

International Journal of Computer Mathematics, 2012
In this paper, we present the explicit expressions of the perturbation of the Drazin inverse under different conditions. Also, we give the upper bounds of ‖(A+E)D−A D‖ P /‖A D‖ P for these cases.
Xiaoji Liu, Shuxia Wu, Yaoming Yu
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Differentiation of the Drazin Inverse

SIAM Journal on Applied Mathematics, 1976
Suppose that A is an $n \times n$ matrix of differentiable functions. Suppose that $A^D $ is defined as $A^D (t) = [ {A(t)} ]^D $ , where $[ {A(t)} ]^D $ is the Drazin inverse of the $n \times n$ matrix $A(t)$. A formula is derived for the derivative of $A^D $ in terms of A, $A^D $ and the derivative of A.
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Some Additive Properties of the Drazin Inverse and Generalized Drazin Inverse

Bulletin of the Iranian Mathematical Society
This paper investigates additive properties of the Drazin inverse and generalized Drazin inverse in a complex Banach algebras \(\mathcal{A}\). The set \(\mathcal{A}^{\text{qnil}}\) consists of all \(a \in \mathcal{A}\) such that \(a\) is quasi-nilpotent, namely, \(\sigma(a) = \{0\}\). Recall that the generalized Drazin inverse of \(a \in \mathcal{A}\),
Fei Peng, Xiaoxiang Zhang
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Challenging Problems on the Perturbation of Drazin Inverse

Annals of Operations Research, 2001
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Yimin Wei 0001, Hebing Wu
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Central Drazin inverses

Journal of Algebra and Its Applications, 2019
We introduce and study a subclass of the Drazin invertible elements in a ring [Formula: see text], which are called central Drazin invertible. An element [Formula: see text] is said to be central Drazin invertible if there exists [Formula: see text] such that [Formula: see text], [Formula: see text] and [Formula: see text] for some integer [Formula ...
Wu, Cang, Zhao, Liang
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The Drazin Inverse of an Infinite Matrix

SIAM Journal on Applied Mathematics, 1976
Let $A = [ {a_{ij} } ]$, $0\leqq i < \infty $, $0\leqq j < \infty $. Then A is called a denumerably infinite matrix. A way to define a Drazin inverse for A is presented. The application of this definition to denumerable Markov chains, infinite linear systems of differential equations, and linear operators on Banach spaces is discussed.
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Perturbation bound of the Drazin inverse

Applied Mathematics and Computation, 2002
The author bounds \(\|(A+E)^D-A^D\|_2\) where \(D\) denotes the Drazin inverse, under assumptions that \(A\) has index \(k\), the rank of \(A+E\) equals the rank of \(A^k\), and \(\|A^D\|_P \|E\|_P
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Structured perturbations of Drazin inverse

Applied Mathematics and Computation, 2004
This work deals with the perturbation theory for Drazin inverse applied to Toeplitz and Hankel structured matrices. The structured condition number is defined in a natural way and its relation with the known condition number of a system \(Ax=b\) is investigated.
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On the Derivative of the Drazin Inverse of a Complex Matrix

SIAM Journal on Mathematical Analysis, 1979
It is shown that the derivative of the Drazin inverse of a differentiable matrix $A(t)$ exists for all values of t in the domain of definition except for the kernels of the nontrivial eigenvalues. Expressions are found for this derivative in terms of the characteristic polynomial, the spectral components and the matrices A, $A^0 $ and $A^d ...
Hartwig, Robert E., Shoaf, Jim
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Block representations of the generalized Drazin inverse

Applied Mathematics and Computation, 2018
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Dijana Mosic, Dragan S. Djordjevic
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