Finding the geometric mean for two Hermitian matrices by an efficient iteration method
Yanlai Song, Fazlollah Soleymani, Ashim Kumar · Mathematical Methods in the Applied Sciences · 2022
In this work, an iterative method is developed to find the matrix sign function. It is discussed in detail that the method is novel in comparison to its competitors from the Padé family of methods for the same purpose. The convergence analysis and the stability of the method are given. The method is then extended to compute the matrix geometric mean of two Hermitian matrices having positive definiteness. This could be employed for solving a Riccati matrix equation, which is of practical importance. Some numerical results are furnished at the end to reveal the effectiveness of the proposed iteration method.