Weighted deterministic walks for the least squares mean on Hadamard spaces | Zendy

Lim Yongdo | Zendy; Pálfia Miklós | Zendy

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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.

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