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Weighted deterministic walks for the least squares mean on Hadamard spaces
Author(s) -
Lim Yongdo,
Pálfia Miklós
Publication year - 2014
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/bdu008
Subject(s) - mathematics , hadamard transform , hadamard matrix , hadamard three lines theorem , hadamard's inequality , hadamard product , complex hadamard matrix , sequence (biology) , combinatorics , space (punctuation) , hadamard's maximal determinant problem , pure mathematics , mathematical analysis , linguistics , philosophy , biology , genetics
We show that the Karcher mean of n points in any Hadamard space can be approximated by a natural explicitly constructed sequence. In the special case when the Hadamard space is the Riemannian manifold of positive definite matrices, this has been recently proved by J. Holbrook. A general version, in which the n points are assigned different weights, is established.