Results 21 to 30 of about 992,721 (210)
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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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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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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The dual index and dual core generalized inverse
Open Mathematics, 2023 In this article, we introduce the dual index and dual core generalized inverse (DCGI). By applying rank equation, generalized inverse, and matrix decomposition, we give several characterizations of the dual index when it is equal to 1. We realize that if
Wang Hongxing, Gao Ju
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Smoothed Analysis of Moore–Penrose Inversion [PDF]
SIAM Journal on Matrix Analysis and Applications, 2010 We perform a smoothed analysis of the condition number of rectangular matrices. We prove that, asymptotically, the expected value of this condition number depends only on the elongation of the matrix and not on the center and variance of the underlying probability distribution.
Peter Bürgisser, Felipe Cucker
openaire +1 more source
Idempotent operator and its applications in Schur complements on Hilbert C*-module
Special Matrices, 2023 The present study proves that TT is an idempotent operator if and only if R(I−T∗)⊕R(T)=X{\mathcal{ {\mathcal R} }}\left(I-{T}^{\ast })\oplus {\mathcal{ {\mathcal R} }}\left(T)={\mathcal{X}} and (T∗T)†=(T†)2T{\left({T}^{\ast }T)}^{\dagger }={\left({T ...
Karizaki Mehdi Mohammadzadeh +1 more
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The Moore-Penrose inverse of a free matrix [PDF]
, 2007 A matrix is free, or generic, if its nonzero entries are algebraically independent.Necessary and sufficient combinatorial conditions are presented for a complex free matrix to have afree Moore-Penrose inverse.
Britz, Thomas
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On the relation between Moore's and Penrose's conditions
International Journal of Mathematics and Mathematical Sciences, 2002 Moore (1920) defined the reciprocal of any matrix over the complex field by three conditions, but the beauty of the definition was not realized until Penrose (1955) defined the same inverse using four conditions.
Gaoxiong Gan
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Fast computing of the Moore-Penrose inverse matrix [PDF]
, 2008 In this article a fast computational method is provided in order to calculate theMoore-Penrose inverse of full rank m × n matrices and of square matrices with at least one zero row or column. Sufficient conditions are also given for special type products
Pappas, Dimitrios +4 more
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