Constructing matrix geometric means
ELA. The Electronic Journal of Linear Algebra, Tome 20 (2010), pp. 419-435.

Voir la notice de l'article dans Electronic Library of Mathematics

Summary: In this paper, we analyze the process of "assembling" new matrix geometric means from existing ones, through function composition or limit processes. We show that for n = 4 a new matrix mean exists which is simpler to compute than the existing ones. Moreover, we show that for n > 4 the existing proving strategies cannot provide a mean computationally simpler than the existing ones.
Classification : 65F30, 15A48, 47A64, 20B35
Mots-clés : matrix geometric mean, positive definite matrix, invariance properties, groups of permutations 
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     author = {Poloni, Federico G.},
     title = {Constructing matrix geometric means},
     journal = {ELA. The Electronic Journal of Linear Algebra},
     pages = {419--435},
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     year = {2010},
     language = {en},
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Poloni, Federico G. Constructing matrix geometric means. ELA. The Electronic Journal of Linear Algebra, Tome 20 (2010), pp. 419-435. https://geodesic-test.mathdoc.fr/item/EEJLA_2010__20__a22/