On the Averaging of Symmetric Positive-Definite Tensors

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Nonsingular $H$-tensor and its criteria (2016, background): “Tensors have wide applications in signal and image processing, continuum physics, higher-order statistics, blind source separation and exploratory multi-way data analysis [4, 16, 22, 25].”
The Closest Elastic Tensor of Arbitrary Symmetry to an Elasticity Tensor of Lower Symmetry (2006, methodology): “3 Elastic distance functions We consider three metrics for Ela: the Euclidean or Frobenius metric dF , the logEuclidean norm dL [2] and the Riemannian metric dR [1].”
Matrix power means and the Karcher mean (2012, background): “This mean has appeared under a variety of other designations: Frechet mean, Cartan mean, Riemannian center of mass [18], Riemannian geometric mean [29], or frequently, Karcher mean [14], the terminology we adopt.”
Computing the Karcher mean of symmetric positive definite matrices (2013, methodology): “, A −1 k , must coincide with G−1 [18].”