Parameterized Wasserstein mean with its properties
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Publication:6317501
DOI10.1016/J.JMAA.2023.127272zbMath1514.15006arXiv1904.09385MaRDI QIDQ6317501
Publication date: 19 April 2019
Abstract: A new least squares mean of positive definite matrices for the divergence associated with the sandwiched quasi-relative entropy has been introduced. It generalizes the well-known Wasserstein mean for covariance matrices of Gaussian distributions with mean zero, so we call it the parameterized Wasserstein mean. We investigate in this article norm inequality of the parameterized Wasserstein mean, give its bounds with respect to the Loewner order, and show the extended version of Lie-Trotter-Kato formula for the parameterized Wasserstein mean. Finally we show the log-majorzation properties of the parameterized Wasserstein mean by using the Cartan mean.
Random matrices (probabilistic aspects) (60B20) Miscellaneous inequalities involving matrices (15A45) Linear transformations, semilinear transformations (15A04) Means on groups, semigroups, etc.; amenable groups (43A07) Operator means involving linear operators, shorted linear operators, etc. (47A64)
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