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Weighted deterministic walks for the least squares mean on Hadamard spaces. (English) Zbl 1291.53050

Summary: 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 [J. Ramanujan Math. Soc. 27, No. 4, 509–521 (2012; Zbl 1325.47039)]. A general version, in which the \(n\) points are assigned different weights, is established.

MSC:

53C20 Global Riemannian geometry, including pinching
53C23 Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces
47A64 Operator means involving linear operators, shorted linear operators, etc.
47B10 Linear operators belonging to operator ideals (nuclear, \(p\)-summing, in the Schatten-von Neumann classes, etc.)

Citations:

Zbl 1325.47039
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References:

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