In this paper, we obtain two refinements of the ordering relations among Heinz means with different parameters via the Taylor series of some hyperbolic functions and by the way, we derive new generalizations of Heinz operator inequalities. Moreover, we establish a matrix version of Heinz inequality for the Hilbert-Schmidt norm. Finally, we introduce a weighted multivariate geometric mean and sh...

The purpose of this paper is to introduce the weighted logarithmic mean two accretive matrices. Among obtained results, we present some inequalities about when involved matrices are sectorial Our approach allowed us derive a new matrix which connected Heinz mean.

A matrix-weighted graph is an undirected with a k×k symmetric positive semidefinite matrix assigned to each edge. Such graphs admit natural generalizations of the Laplacian and adjacency matrices, leading generalized notion expansion. Extensions some theorems about expansion hold for graphs—in particular, analogue expander mixing lemma one half Cheeger-type inequality. These results lead defini...

Abstract Finite mixtures of regressions with fixed covariates are a commonly used model-based clustering methodology to deal regression data. However, they assume assignment independence, i.e., the allocation data points clusters is made independently distribution covariates. To take into account latter aspect, finite random covariates, also known as cluster-weighted models (CWMs), have been pr...

Weighted averages of Kiefer–Wolfowitz-type procedures, which are driven by larger step lengths than usual, can achieve the optimal rate of convergence. A priori knowledge of a lower bound on the smallest eigenvalue of the Hessian matrix is avoided. The asymptotic mean squared error of the weighted averaging algorithm is the same as would emerge using a Newton-type adaptive algorithm. Several di...

This article investigates discrete-time matrix-weighted consensus of multi-agent networks over undirected and connected graphs. We first present protocols for the agents in common symmetric matrix weights with possibly different update rates switching network topologies. A special type non-symmetric matrix-weights that can render several control scenarios such as ones scaled/rotated updates aff...