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Linear Algebra and its Applications, 2004 Let \(G(A,B)\) be the geometric mean of two \(n\times n\) positive semidefinite matrices \(A\) and \(B\). The authors extend the definition of \(G\) to any number of \(n\times n\) positive semidefinite matrices inductively. Suppose that for some \(k\geq 2\), the geometric mean \(G(A_1,A_2,\dots,A_k)\) of any \(k\) positive semidefinite matrices \(A_1 ...
Ando, T., Li, Chi-Kwong, Mathias, Roy
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Two Sharp Inequalities for Power Mean, Geometric Mean, and Harmonic Mean
Journal of Inequalities and Applications, 2009 For p∈R, the power mean of order p of two positive numbers a and b is defined by Mp(a,b)=((ap+bp)/2)1/p,p≠0, and Mp(a,b)=ab, p=0.
Wei-Feng Xia, Yu-Ming Chu
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Joint Access Configuration and Beamforming for Cell-Free Massive MIMO Systems With Dynamic TDD
IEEE Access, 2022 We address the trade-off between system throughput and user equipment (UE) fairness in dynamic time division duplex (TDD) cell-free (CF)-massive multiple-input multiple-output (mMIMO) systems, developing to that end a joint access point (AP) access ...
Shuto Fukue +3 more
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The Multi-Objective Transportation Problem Solve with Geometric Mean and Penalty Methods
Indonesian Journal of Innovation and Applied Sciences, 2023 The traditional (classical) Transportation Problem (TP) can be viewed as a specific case of the Linear Programming (LP) problem, as well as its models are used to find the best solution for the problem of predetermined how many units of a good or service
K.P.O.Niluminda, E.M.U.S.B.Ekanayake
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Sharp bounds for Gauss Lemniscate functions and Lemniscatic means
AIMS Mathematics, 2021 For $ a, b > 0 $ with $ a\neq b $, the Gauss lemniscate mean $ \mathcal{LM}(a, b) $ is defined by $ \begin{equation*} \mathcal{LM}(a,b) = \left\{\begin{array}{lll} \frac{\sqrt{a^2-b^2}}{\left[{ {\rm{arcsl}}}\left(\sqrt[4]{1-b^2/a^2}\right)\right]^2}
Wei-Mao Qian, Miao-Kun Wang
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Mean Estimation on the Diagonal of Product Manifolds
Algorithms, 2022 Computing sample means on Riemannian manifolds is typically computationally costly, as exemplified by computation of the Fréchet mean, which often requires finding minimizing geodesics to each data point for each step of an iterative optimization scheme.
Mathias Højgaard Jensen, Stefan Sommer
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Arithmetic-Geometric Mean Robustness for Control from Signal Temporal Logic Specifications [PDF]
American Control Conference, 2019 We present a new average-based robustness for Signal Temporal Logic (STL) and a framework for optimal control of a dynamical system under STL constraints.
N. Mehdipour, C. Vasile, C. Belta
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A Riemannian Limited-Memory BFGS Algorithm for Computing the Matrix Geometric Mean
International Conference on Conceptual Structures, 2016 Xinru Yuan +3 more
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Diffusion means in geometric spaces [PDF]
Bernoulli, 2023 We introduce a location statistic for distributions on non-linear geometric spaces, the diffusion mean, serving as an extension and an alternative to the Fréchet mean. The diffusion mean arises as the generalization of Gaussian maximum likelihood analysis to non-linear spaces by maximizing the likelihood of a Brownian motion. The diffusion mean depends
Eltzner, Benjamin +3 more
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Optimal convex combination bounds of geometric and Neuman means for Toader-type mean
Journal of Inequalities and Applications, 2017 In this paper, we prove that the double inequalities α N Q A ( a , b ) + ( 1 − α ) G ( a , b ) < T D [ A ( a , b ) , G ( a , b ) ] < β N Q A ( a , b ) + ( 1 − β ) G ( a , b ) , λ N A Q ( a , b ) + ( 1 − λ ) G ( a , b ) < T D [ A ( a , b ) , G ( a , b ) ]
Yue-Ying Yang, Wei-Mao Qian
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