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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 ...
Georg Heinig, Frank Hellinger
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A note on stable perturbations of Moore–Penrose inverses
Numerical Linear Algebra with Applications, 2011SUMMARYPerturbation bounds for Moore–Penrose inverses of rectangular matrices play a significant role in the perturbation analysis for linear least squares problems. In this note, we derive a sharp upper bound for Moore–Penrose inverses, which is better than a well known existing one. Copyright © 2011 John Wiley & Sons, Ltd.
Zhao Li, Qingxiang Xu, Yimin Wei 0001
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Projections generated by Moore–Penrose inverses and core inverses
Journal of Algebra and Its Applications, 2020Let [Formula: see text] be a unital ∗-ring. As is well known, idempotents and projections can be constructed by the Moore–Penrose inverse and the core inverse of an element in [Formula: see text]. In this paper, we mainly investigate characterizations and properties of these types of idempotents and projections.
Huihui Zhu, Fei Peng
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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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Approximating the inverse and the Moore‐Penrose inverse of complex matrices
Mathematical Methods in the Applied Sciences, 2019A parametric family of fourth‐order schemes for computing the inverse and the Moore‐Penrose inverse of a complex matrix is designed. A particular value of the parameter allows us to obtain a fifth‐order method. Convergence analysis of the different methods is studied. Every iteration of the proposed schemes involves four matrix multiplications.
Alicia Cordero +2 more
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On the Moore--Penrose inverse of a closed linear relation
Publicationes Mathematicae Debrecen, 2014Summary: For a closed multivalued linear operator \(T\) between complex Hilbert spaces, the concept of Moore-Penrose inverse of \(T\), denoted \(T^\dagger\), is introduced and studied. We prove that if \(y\in D(T^\dagger)\), then \(T^\dagger y\) is the least square solution of minimal norm of the relation equation \(y \in Tx\). We also approximate \(T^\
Teresa Alvarez, Qiaoling Xia
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Moore--Penrose Inverse of Matrices on Idempotent Semirings
SIAM Journal on Matrix Analysis and Applications, 2000The author gives necessary and sufficient conditions on a matrix \(A\) over a commutative, algebraically complete semiring in which the cancellation and stabilization condition holds and in which \(\oplus \) is idempotent and the partial ordering ``\(\leq\)'' induced by \(\oplus\) is total so that it admits a Moore-Penrose inverse.
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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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