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Concavity of weighted arithmetic means with applications

✍ Scribed by Arkady Berenstein; Alek Vainshtein


Publisher
Springer
Year
1997
Tongue
English
Weight
172 KB
Volume
69
Category
Article
ISSN
0003-889X

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We define a new family of matrix means {L ΞΌ (Ο‰; A)} μ∈R where Ο‰ and A vary over all positive probability vectors in R m and m-tuples of positive definite matrices resp. Each of these means interpolates between the weighted harmonic mean (ΞΌ = -∞) and the arithmetic mean of the same weight (ΞΌ = ∞) wit