Positive definite matrices play a central role in mathematics, physics, statistics and engineering due to their unique properties and widespread applicability. These matrices, which are characterised ...

A shift splitting concept is introduced and, correspondingly, a shift-splitting iteration scheme and a shift-splitting preconditioner are presented, for solving the large sparse system of linear ...

A new class of large-sample covariance and spectral density matrix estimators is proposed based on the notion of flat-top kernels. The new estimators are shown to be higher-order accurate when ...

This book represents the first synthesis of the considerable body of new research into positive definite matrices. These matrices play the same role in noncommutative analysis as positive real numbers ...

Abstract: The goal of this paper is to leverage more information from a single measurement (e.g. an ElectroEncephalo-Graphic (EEG) trial) by representing it as a trajectory of covariance matrices ...

Left: Illustration of different geometric mean properties on the manifold of positive semidefinite matrices implemented in this library. Deviation of the geometric means computed using the ...