A majorization-minimization (MM) algorithm for the Karcher mean of np× p positive definite
matrices is proposed and it is gauranteed to converge linearly. Simulations show that the …

This paper considers the computation of the matrix exponential $\mathrm {e}^ A $ with
numerical quadrature. Although several quadrature-based algorithms have been proposed …

The aim of this study is to find the Moore–Penrose inverse of rectangular matrices
numerically. To achieve this, we present a new iteration for matrix inversion in a general …

We investigate different approaches for computing the action of the weighted geometric
mean of two large-scale positive definite matrices on a vector. We derive and analyze …

In the present paper, we first introduce a block variant of the Hessenberg process and
discuss its properties. Then, we show how to apply the block Hessenberg process in order to …

A new definition is introduced for the matrix geometric mean of a set of k positive definite n×
n matrices together with an iterative method for its computation. The iterative method is …

Bai et al. proposed the multistep Rayleigh quotient iteration (MRQI) as well as its inexact
variant (IMRQI) in a recent work (Comput. Math. Appl. 77: 2396–2406, 2019). These …

In the HSS iteration methods proposed by Bai, Golub and Ng [Z.-Z. Bai, GH Golub, MK Ng,
Hermitian and skew-Hermitian splitting methods for non-Hermitian positive definite linear …

The set of Hermitian positive-definite matrices plays fundamental roles in many disciplines
such as mathematics, numerical analysis, probability and statistics, engineering, and …

We propose a quadratically convergent algorithm for computing the invariant subspaces of
an Hermitian matrix. Each iteration of the algorithm consists of one matrix-matrix …