94 citations · 128 across the 14 of their papers we have counts for
8 papers · 1 filter
Weak log-majorization between the geometric and Wasserstein means
Luyining Gan, Sejong Kim
There exist lots of distinct geometric means on the cone of positive definite Hermitian matrices such as the metric geometric mean, spectral geometric mean, log-Euclidean mean and…
Revisit on spectral geometric mean
Luyining Gan, Sejong Kim
In this paper we introduce the limit, unique solution of the nonlinear equations, geodesic property, tolerance relations and pinch on the spectral geometric mean for two positive d…
Mixture and interpolation of the parameterized ordered means
Sejong Kim
Loewner partial order plays a very important role in metric topology and operator inequality on the open convex cone of positive invertible operators. In this paper we consider a f…
Operator inequalities and gyrolines of the weighted geometric means
Sejong Kim
We consider in this paper two different types of the weighted geometric means of positive definite operators. We show the component-wise bijection of these geometric means and give…
Tensor product and Hadamard product for the Wasserstein means
Jinmi Hwang, Sejong Kim
As one of the least squares mean, we consider the Wasserstein mean of positive definite Hermitian matrices. We verify in this paper the inequalities of the Wasserstein mean related…
Parameterized Wasserstein mean with its properties
Sejong Kim
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 W…
Geometric Mean of Partial Positive Definite Matrices with Missing Entries
Hayoung Choi, Sejong Kim, Yuanming Shi
In this paper the geometric mean of partial positive definite matrices with missing entries is considered. The weighted geometric mean of two sets of positive matrices is defined,…
Bounds for the Wasserstein mean with applications to the Lie-Trotter mean
Jinmi Hwang, Sejong Kim
As the least squares mean for the Riemannian trace metric on the cone of positive definite matrices, the Riemannian mean with its computational and theoretical approaches has been…