An Algorithm for Computing Geometric Mean of Two Hermitian Positive Definite Matrices via Matrix Sign-Reference-Cited by-同舟云学术

An Algorithm for Computing Geometric Mean of Two Hermitian Positive Definite Matrices via Matrix Sign

Published:2014 Issue: Volume:2014 Page:1-6
ISSN:1085-3375
Container-title:Abstract and Applied Analysis
language:en
Short-container-title:Abstract and Applied Analysis

Author:

Soleymani F.¹,Sharifi M.¹,Shateyi S.²,Khaksar Haghani F.¹

Affiliation:

1. Department of Mathematics, Islamic Azad University, Shahrekord Branch, Shahrekord, Iran

2. Department of Mathematics and Applied Mathematics, School of Mathematical and Natural Sciences, University of Venda, Private Bag X5050, Thohoyandou 0950, South Africa

Abstract

Using the relation between a principal matrix square root and its inverse with the geometric mean, we present a fast algorithm for computing the geometric mean of two Hermitian positive definite matrices. The algorithm is stable and possesses a high convergence order. Some experiments are included to support the proposed computational algorithm.

Publisher

Hindawi Limited

Subject

Applied Mathematics,Analysis

Link

http://downloads.hindawi.com/journals/aaa/2014/978629.pdf

Reference16 articles.

1. Functional calculus for sesquilinear forms and the purification map

2. A note on computing matrix geometric means

3. The palindromic cyclic reduction and related algorithms

Cited by 7 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. An Efficient Iterative Approach for Hermitian Matrices Having a Fourth-Order Convergence Rate to Find the Geometric Mean;Mathematics;2024-06-06

2. Riccati equation and metric geometric means of positive semidefinite matrices involving semi-tensor products;AIMS Mathematics;2023

3. An Integrated Approach for Developing an Urban Livability Composite Index—A Cities’ Ranking Road Map to Achieve Urban Sustainability;Sustainability;2022-07-18

4. A New Inversion-Free Iterative Scheme to Compute Maximal and Minimal Solutions of a Nonlinear Matrix Equation;Mathematics;2021-11-23

5. A fast iterative method to find the matrix geometric mean of two HPD matrices;Mathematical Methods in the Applied Sciences;2019-07-11