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Moore–Penrose Inversion of Square Toeplitz Matrices
SIAM Journal on Matrix Analysis and Applications, 1994The algorithms presented in this paper are based on a matrix representation for the Moore-Penrose inverses of square Toeplitz matrices given by the authors [ibid. 14, No. 3, 629-645 (1993; Zbl 0782.15003)]. Two approaches are given. The first is based on a recursion of nested matrices and the second uses generalized inverses of Toeplitz matrices that ...
Heinig, Georg, Hellinger, Frank
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Perturbation Analysis of the Moore-Penrose Inverse and the Weighted Moore-Penrose Inverse
2018Let A be a given matrix. When computing a generalized inverse of A, due to rounding error, we actually obtain the generalized inverse of a perturbed matrix \(B=A+E\) of A. It is natural to ask if the generalized inverse of B is close to that of A when the perturbation E is sufficiently small.
Guorong Wang, Yimin Wei, Sanzheng Qiao
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1997
By definition, a generalized inverse of an m × n matrix A is any n × m matrix G such that AGA = A. Except for the special case where A is a (square) nonsingular matrix, A has an infinite number of generalized inverses (as discussed in Section 9.2a).
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By definition, a generalized inverse of an m × n matrix A is any n × m matrix G such that AGA = A. Except for the special case where A is a (square) nonsingular matrix, A has an infinite number of generalized inverses (as discussed in Section 9.2a).
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On the Moore–Penrose generalized inverse matrix
Applied Mathematics and Computation, 2004Different methods for computing the Moore-Penrose inverse (MPI) matrix are reviewed. For the MPI of a matrix product, four mixed type reverse order laws are established. Some relevant numerical computations are given.
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The generalized weighted Moore-Penrose inverse
Journal of Applied Mathematics and Computing, 2007The generalized weighted Moore-Penrose inverse is introduced as a generalization of the well-known weighted Moore-Penrose inverse. The authors study this new kind of matrices analyzing the existence, uniqueness and its representation.
Sheng, Xingping, Chen, Guoliang
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More on Moore-Penrose Inverses
1979The various properties of A+ discussed in this section are fundamental to the theory of Moore-Penrose inverses. In many cases, proofs simply require verification that the defining equations in (2.2) are satisfied for A and some particular matrix X.
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Moore-Penrose Inverses and Singular Values
1999Let H be a Hilbert space and let A be a bounded linear operator on H. Then sp A*A ⊂[0,∞), and the non-negative square roots of the numbers in sp A*A are called the singular values of A. The set of the singular values of A will be denoted byΣ(A), $$ \sum {\left( A \right)} : = \left\{ {s \in \left[ {\left.
Albrecht Böttcher, Bernd Silbermann
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Moore-Penrose Inverse of Linear Operators
2018Before Moore introduced the generalized inverse of matrices by algebraic methods, Fredholm, Hilbert, Schmidt, Bounitzky, Hurwitz and other mathematicians had studied the generalized inverses of integral operators and differential operators. Recently, due to the development of science and technology and the need for practical problems, researchers are ...
Guorong Wang, Yimin Wei, Sanzheng Qiao
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Moore-Penrose Inverse in Kreĭn Spaces
Integral Equations and Operator Theory, 2008We discuss the notion of Moore-Penrose inverse in Kreĭn spaces for both bounded and unbounded operators. Conditions for the existence of a Moore-Penrose inverse are given. We then investigate its relation with adjoint operators, and study the involutive Banach algebra \({\mathfrak{B}}({\mathcal{H}})\).
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