Computing the Matrix Geometric Mean of Two HPD Matrices: A Stable Iterative Method

Subject Areas : International Journal of Industrial Mathematics

F. Kiyoumarsi ^{1 *}

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

Received: 2017-05-13 Accepted : 2018-05-18 Published : 2020-01-01

Keywords: Stability, Sign function, HPD, Convergence, Iterative methods,

Abstract :

A new iteration scheme for computing the sign of a matrix which has no pure imaginary eigenvalues is presented. Then, by applying a well-known identity in matrix functions theory, an algorithm for computing the geometric mean of two Hermitian positive definite matrices is constructed. Moreover, another efficient algorithm for this purpose is derived free from the computation of principal matrix square root. Finally, several experiments are collected.

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