Using Jacobi field arguments, this paper describes an iterative procedure for finding the Riemannian barycentres of a class of probability measures on complete, simply connected Riemannian manifolds with a finite upper bound on their sectional curvatures. This, in particular, generalises an earlier result of the author's (‘Locating Fréchet means with application to shape spaces’, Adv. Appl. Probab. 33 (2001) 324-338).
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Huiling Le (2004) studied this question.
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