The resolvent average on symmetric cones
type: Item
instance of: scholarly article
title: The resolvent average on symmetric cones
zbMATH Open document ID: 1271.17023
author: Sangho Kum
author: Yongdo Lim
published in: Linear Algebra and its Applications
publication date: 2013-01-16T00:00:00Z
review text: Let \(V\) be an Euclidean Jordan algebra with identity \(e\), let \(\Omega \) be the interior of the set of all square elements of \(V\), let \(\Delta _{m}\) be the set of all probability vectors in \(\mathbb{R}^{m}\) with strictly positive components, and let \(\mu \geq 0\). The authors study the resolvent average of \(\mathbf{a}=(a_{1},\dots,a_{m})\in \Omega ^{m}\) with weight vector \(\omega =(w_{1},\dots,w_{m})\in \Delta _{m}\), defined by \(R_{\mu }(\omega ;\mathbf{a})=[\sum_{i=1}^{m}w_{i}(a_{i}+\mu e)^{-1}]^{-1}-\mu e\); for \(\mu =\infty\), one sets \(R_{\infty }(\omega ;\mathbf{a})=\sum_{i=1}^{m}w_{i}a_{i}\). This notion extends the corresponding one for positive semidefinite matrices introduced by \textit{H. H. Bauschke, S. M. Moffat} and \textit{X. Wang} [Linear Algebra Appl. 432, No. 7, 1757--1771 (2010; Zbl 1191.15024)].
Mathematics Subject Classification ID: 17C50
Mathematics Subject Classification ID: 26B25
Mathematics Subject Classification ID: 52A41
zbMATH DE Number: 6125855
zbMATH Keywords: symmetric cone
zbMATH Keywords: resolvent average
zbMATH Keywords: convex analysis
zbMATH Keywords: Euclidean Jordan algebra
reviewed by: Juan-Enrique Martínez-Legaz
MaRDI profile type: Publication
full work available at URL: j.laa.2012.09.005
OpenAlex ID: W1979021956
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DOI: 10.1016/J.LAA.2012.09.005
description: scientific article; zbMATH DE number 6125855