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Expressions and characterizations for the Moore-Penrose inverse [PDF]
, 2023 Under certain conditions, we prove that the Moore-Penrose inverse of a sum of operators is the sum of the Moore-Penrose inverses. From this, we derive expressions and characterizations for the Moore-Penrose inverse of an operator that are useful for its ...
Patricia Morillas +2 more
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Existence of Moore-Penrose inverses in rings with involution [PDF]
Songklanakarin Journal of Science and Technology (SJST), 2018 We give necessary and sufficient conditions for the existence of the Moore-Penrose inverse of an element in a ring with involution. If R is a ring with involution, we also investigate the existence of the Moore-Penrose inverse of the product 1 2 n x
Wannisa Apairat, Sompong Chuysurichay
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IEEE Access, 2023 The computation of the Moore–Penrose generalized inverse is a commonly used operation in various fields such as the training of neural networks based on random weights.
Elkin Gelvez-Almeida +3 more
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On the perturbation of the Moore–Penrose inverse of a matrix [PDF]
Applied Mathematics and Computation, 2020 The Moore-Penrose inverse of a matrix has been extensively investigated and widely applied in many fields over the past decades. One reason for the interest is that the Moore-Penrose inverse can succinctly express some important geometric constructions in finite-dimensional spaces, such as the orthogonal projection onto a subspace and the linear least ...
openaire +2 more sources
A Neural Network for Moore–Penrose Inverse of Time-Varying Complex-Valued Matrices
International Journal of Computational Intelligence Systems, 2020 The Moore–Penrose inverse of a matrix plays a very important role in practical applications. In general, it is not easy to immediately solve the Moore–Penrose inverse of a matrix, especially for solving the Moore–Penrose inverse of a complex-valued ...
Yiyuan Chai +4 more
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Calculating the Moore–Penrose Generalized Inverse on Massively Parallel Systems
Algorithms, 2022 In this work, we consider the problem of calculating the generalized Moore–Penrose inverse, which is essential in many applications of graph theory.
Vukašin Stanojević +4 more
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Convergence of Rump's method for computing the Moore-Penrose inverse [PDF]
, 2016 summary:We extend Rump's verified method (S. Oishi, K. Tanabe, T. Ogita, S. M. Rump (2007)) for computing the inverse of extremely ill-conditioned square matrices to computing the Moore-Penrose inverse of extremely ill-conditioned rectangular matrices ...
Chen, Yunkun, Wei, Yimin, Shi, Xinghua
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Weighted Moore-Penrose inverse of a boolean matrix [PDF]
, 1997 If A is a boolean matrix, then the weighted Moore-Penrose inverse of A (with respect to the given matrices M, N) is a matrix G which satisfies AGA = A, GAG = G, and that MAG and GAN are symmetric.
S.K. Jain +5 more
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On the mean and variance of the estimated tangency portfolio weights for small samples
Modern Stochastics: Theory and Applications, 2022 In this paper, a sample estimator of the tangency portfolio (TP) weights is considered. The focus is on the situation where the number of observations is smaller than the number of assets in the portfolio and the returns are i.i.d.
Gustav Alfelt, Stepan Mazur
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Moore–Penrose inverse of set inclusion matrices [PDF]
, 2000 Given integers s,k and v, let Wsk be the vs×vk 0–1 matrix, the rows and the columns of which are indexed by the s-subsets and the k-subsets of a v-set respectively, and where the entry in row S and column U is 1 if S⊂U and 0 otherwise.
R.B. Bapat, Bapat, R. B., Bapat, R.B.
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