An algorithm for computing geometric mean of two Hermitian positive definite matrices via matrix sign. (English) Zbl 1474.65123

Summary: 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.


65F60 Numerical computation of matrix exponential and similar matrix functions
15A60 Norms of matrices, numerical range, applications of functional analysis to matrix theory
15B48 Positive matrices and their generalizations; cones of matrices
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