Pitrik, József and Virosztek, Dániel (2021) A divergence center interpretation of general symmetric Kubo-Ando means, and related weighted multivariate operator means. LINEAR ALGEBRA AND ITS APPLICATIONS, 609. pp. 203-217. ISSN 0024-3795
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Abstract
It is well known that special Kubo-Ando operator means admit divergence center interpretations, moreover, they are also mean squared error estimators for certain metrics on positive definite operators. In this paper we give a divergence center interpretation for every symmetric Kubo-Ando mean. This characterization of the symmetric means naturally leads to a definition of weighted and multivariate versions of a large class of symmetric Kubo-Ando means. We study elementary properties of these weighted multivariate means, and note in particular that in the special case of the geometric mean we recover the weighted A#H-mean introduced by Kim, Lawson, and Lim.
| Item Type: | Article |
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| Uncontrolled Keywords: | Mathematical techniques; Mean square error; Linear algebra; Geometric mean; barycenter; Kubo–Ando mean; Positive definite; mean squared error; Weighted multivariate mean; |
| Subjects: | Q Science / természettudomány > QA Mathematics / matematika |
| SWORD Depositor: | MTMT SWORD |
| Depositing User: | MTMT SWORD |
| Date Deposited: | 04 Jan 2021 13:53 |
| Last Modified: | 25 Apr 2023 07:03 |
| URI: | http://real.mtak.hu/id/eprint/119094 |
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