Results 101 to 110 of about 146 (131)

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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Operator Drazin Inverse

2018
Let X be a Hilbert space and L(X) be the vector space of the linear operators from X into X. We denote the set of bounded linear operators from X into X by B(X). In this chapter, we will investigate the definition, basic properties, representation theorem and computational methods for the Drazin inverse of an operator \(T \in B(X)\), \(\mathcal {R}(T^k)
Guorong Wang, Yimin Wei, Sanzheng Qiao
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An expression of the Drazin inverse of a perturbed matrix

Applied Mathematics and Computation, 2004
It is well-known that the perturbation theory of the Drazin inverse \(A^D\) is much more complicated than that of the group inverse \(A^{\sharp}\), which coincides with \(A^D\) in the case where ind\((A)=1\). The constraint ind\((A)=1\) allows to achieve some good upper bounds on relative perturbation error.
Xiezhang Li, Yimin Wei 0001
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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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Continuity of The Drazin inverse

Linear and Multilinear Algebra, 1980
Let A be an n×n matrix. It is shown that if a matrix  comes close to satisfying the definition of the Drazin inverse of A,AD , then  is close to AD .
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An improvement on perturbation bounds for the Drazin inverse

Numerical Linear Algebra with Applications, 2003
AbstractThe Drazin inverse of a square matrix occurs in a number of applications. It is of importance to analyse the perturbation bounds for the Drazin inverse of a matrix. Let B=A+E. Under the assumption of rank(Bj) =rank(Ak), where j and k are the indices of B and A, respectively, upper bounds of ∥BD‐AD∥/∥AD∥ and ∥BBD‐AAD∥/∥AAD∥ have been recently ...
Yimin Wei 0001, Xiezhang Li
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Representation and approximation for the Drazin inverse A(d)

Applied Mathematics and Computation, 2001
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Extensions of Jacobson’s lemma for Drazin inverses

Aequationes mathematicae, 2017
Let \(R\) be a ring with an identity. The Jacobson's lemma states that if \(a,b\in R\) and \(1-ab\) is an invertible element, then \(1-ba\) is also an invertible element and \((1-ba)^{-1}= 1+b(1-ab)^{-1}a\). In this paper, the author uses the following concepts: group invertible elements of \(R\), Drazin invertible, generalized Drazin invertible ...
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A Representation of the Drazin Inverse and Characterizations of the Index

SIAM Journal on Applied Mathematics, 1976
A representation for the Drazin inverse of an arbitrary square matrix in terms of the eigenprojection is established in this paper. The Laurent expansion of the resolvent of our matrix has coefficients (for the nonnegative indices) which are powers of the Drazin inverse.
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