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<p>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.</p>

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

  • 期刊论文

  • 发表日期：

    2025年2月18日

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  • Pallvi Sharma,
  • Munish Kansal

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.