An Iterative Formulation to Compute the Matrix Sign Function and Its Application in Evaluating the Geometric Mean of Hermitian Positive Definite Matrices

被引：0

作者：

Sharma, Pallvi ^{[1
]}

Kansal, Munish ^{[1
]}

机构：

[1] Thapar Inst Engn & Technol, Dept Math, Patiala 147004, Punjab, India

来源：

MEDITERRANEAN JOURNAL OF MATHEMATICS | 2025年 / 22卷 / 02期

关键词：

Matrix sign function; basins of attraction; global convergence; iterative methods; geometric mean;

D O I：

10.1007/s00009-025-02807-4

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this research, a new matrix iterative method with a convergence order four is proposed for computing the sign function of a complex matrix having no eigenvalue on the imaginary axis. Convergence of the proposed method has been discussed globally along with the illustration of attraction basins. Asymptotic stability of the method is also presented. Then, an application of the matrix sign function has been demonstrated by computing the geometric mean of two Hermitian positive definite matrices. Several numerical experiments have been performed to justify the effectiveness of the proposed method by considering matrices of different sizes.

引用

页数：23

共 10 条

[1] An Algorithm for Computing Geometric Mean of Two Hermitian Positive Definite Matrices via Matrix Sign
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[9] Dimensionality reduction based on distance preservation to local mean for symmetric positive definite matrices and its application in brain-computer interfaces
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[10] A matrix pseudo-inversion lemma for positive semidefinite hermitian matrices and its application to adaptive blind deconvolution of MIMO systems
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