Weighted geometric means
Copyright policy )Weighted geometric means
In the recent years, many authors have discussed the geometric mean of \(n\) positive definite matrices. We have three types of geometric means which have at least ten nice properties. One of them is called BMP mean, which is defined by using symmetrization procedures [\textit{D. A. Bini}, \textit{B. Meini} and \textit{F. Poloni}, Math. Comput. 79, No. 269, 437--452 (2010; Zbl 1194.65065)]. The authors extend here the notion of BMP mean for positive definite matrices into one for a general convex metric space. Moreover, the authors consider the weighted BMP mean of \(n\)-elements in the convex metric spaces.
- Louisiana State University United States
- Kyungpook National University Korea (Republic of)
positive definite matrix, Positive matrices and their generalizations; cones of matrices, Operator means involving linear operators, shorted linear operators, etc., Metric spaces, metrizability, Bini-Meini-Poloni symmetrization procedure, convex metric, weighted mean, Metric geometry, matrix geometric mean
positive definite matrix, Positive matrices and their generalizations; cones of matrices, Operator means involving linear operators, shorted linear operators, etc., Metric spaces, metrizability, Bini-Meini-Poloni symmetrization procedure, convex metric, weighted mean, Metric geometry, matrix geometric mean
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