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arXiv · 2407.07438

Near-order relation of power means

Jinmi Hwang·Sejong Kim
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Abstract

On the setting of positive definite operators we study the near-order properties of power means such as the quasi-arithmetic mean (H\"{o}lder mean) and R\'{e}nyi power mean. We see the monotonicity of spectral geometric mean and Wasserstein mean on parameters with respect to the near-order and the near-order relationship between the spectral geometric mean and Wasserstein mean. Furthermore, the monotonicity of quasi-arithmetic mean on parameters and the convergence of R\'{e}nyi power mean to the log-Euclidean mean with respect to the near-order have been established.

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Jinmi Hwang, Sejong Kim. 2024-07-10. Near-order relation of power means. https://arxiv.org/abs/2407.07438

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