{"publication_status":"published","external_id":{"arxiv":["2002.11678"],"isi":["000581730500011"]},"year":"2021","volume":609,"publisher":"Elsevier","day":"15","oa":1,"language":[{"iso":"eng"}],"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2002.11678"}],"date_updated":"2023-08-04T10:58:14Z","publication":"Linear Algebra and its Applications","_id":"8373","doi":"10.1016/j.laa.2020.09.007","page":"203-217","acknowledgement":"The authors are grateful to Milán Mosonyi for fruitful discussions on the topic, and to the anonymous referee for his/her comments and suggestions.\r\nJ. Pitrik was supported by the Hungarian Academy of Sciences Lendület-Momentum Grant for Quantum Information Theory, No. 96 141, and by Hungarian National Research, Development and Innovation Office (NKFIH) via grants no. K119442, no. K124152, and no. KH129601. D. Virosztek was supported by the ISTFELLOW program of the Institute of Science and Technology Austria (project code IC1027FELL01), by the European Union's Horizon 2020 research and innovation program under the Marie Sklodowska-Curie Grant Agreement No. 846294, and partially supported by the Hungarian National Research, Development and Innovation Office (NKFIH) via grants no. K124152, and no. KH129601.","title":"A divergence center interpretation of general symmetric Kubo-Ando means, and related weighted multivariate operator means","status":"public","ec_funded":1,"month":"01","type":"journal_article","publication_identifier":{"issn":["0024-3795"]},"article_processing_charge":"No","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","article_type":"original","date_created":"2020-09-11T08:35:50Z","oa_version":"Preprint","keyword":["Kubo-Ando mean","weighted multivariate mean","barycenter"],"date_published":"2021-01-15T00:00:00Z","quality_controlled":"1","abstract":[{"text":"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.","lang":"eng"}],"project":[{"name":"Geometric study of Wasserstein spaces and free probability","call_identifier":"H2020","grant_number":"846294","_id":"26A455A6-B435-11E9-9278-68D0E5697425"},{"call_identifier":"FP7","name":"International IST Postdoc Fellowship Programme","grant_number":"291734","_id":"25681D80-B435-11E9-9278-68D0E5697425"}],"author":[{"last_name":"Pitrik","full_name":"Pitrik, József","first_name":"József"},{"full_name":"Virosztek, Daniel","last_name":"Virosztek","first_name":"Daniel","orcid":"0000-0003-1109-5511","id":"48DB45DA-F248-11E8-B48F-1D18A9856A87"}],"citation":{"chicago":"Pitrik, József, and Daniel Virosztek. “A Divergence Center Interpretation of General Symmetric Kubo-Ando Means, and Related Weighted Multivariate Operator Means.” <i>Linear Algebra and Its Applications</i>. Elsevier, 2021. <a href=\"https://doi.org/10.1016/j.laa.2020.09.007\">https://doi.org/10.1016/j.laa.2020.09.007</a>.","ieee":"J. Pitrik and D. Virosztek, “A divergence center interpretation of general symmetric Kubo-Ando means, and related weighted multivariate operator means,” <i>Linear Algebra and its Applications</i>, vol. 609. Elsevier, pp. 203–217, 2021.","mla":"Pitrik, József, and Daniel Virosztek. “A Divergence Center Interpretation of General Symmetric Kubo-Ando Means, and Related Weighted Multivariate Operator Means.” <i>Linear Algebra and Its Applications</i>, vol. 609, Elsevier, 2021, pp. 203–17, doi:<a href=\"https://doi.org/10.1016/j.laa.2020.09.007\">10.1016/j.laa.2020.09.007</a>.","apa":"Pitrik, J., &#38; Virosztek, D. (2021). A divergence center interpretation of general symmetric Kubo-Ando means, and related weighted multivariate operator means. <i>Linear Algebra and Its Applications</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.laa.2020.09.007\">https://doi.org/10.1016/j.laa.2020.09.007</a>","ista":"Pitrik J, Virosztek D. 2021. A divergence center interpretation of general symmetric Kubo-Ando means, and related weighted multivariate operator means. Linear Algebra and its Applications. 609, 203–217.","short":"J. Pitrik, D. Virosztek, Linear Algebra and Its Applications 609 (2021) 203–217.","ama":"Pitrik J, Virosztek D. A divergence center interpretation of general symmetric Kubo-Ando means, and related weighted multivariate operator means. <i>Linear Algebra and its Applications</i>. 2021;609:203-217. doi:<a href=\"https://doi.org/10.1016/j.laa.2020.09.007\">10.1016/j.laa.2020.09.007</a>"},"intvolume":"       609","isi":1,"department":[{"_id":"LaEr"}]}