The resolvent average for positive semidefinite matrices

被引：21

作者：

Bauschke, Heinz H. ^{[1
]}

Moffat, Sarah M. ^{[1
]}

Wang, Xianfu ^{[1
]}

机构：

[1] Univ British Columbia Okanagan, Irving K Barber Sch, Dept Math, Kelowna, BC V1V 1V7, Canada

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2010年 / 432卷 / 07期

基金：

加拿大自然科学与工程研究理事会;

关键词：

Arithmetic average; Arithmetic mean; Convex function; Fenchel conjugate; Geometric mean; Harmonic average; Harmonic mean; Positive semi-definite matrix; Proximal average; Resolvent average; Subdifferential; PARALLEL ADDITION; MONOTONE; GEOMETRY;

D O I：

10.1016/j.laa.2009.11.028

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We define a new average - termed the resolvent average - for positive semidefinite matrices. For positive definite matrices, the resolvent average enjoys self-duality and it interpolates between the harmonic and the arithmetic averages, which it approaches when taking appropriate limits. We compare the resolvent average to the geometric mean. Some applications to matrix functions are also given. (C) 2009 Elsevier Inc. All rights reserved.

引用

页码：1757 / 1771

页数：15

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