Efficient algorithms for inferences on Grassmann manifolds

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On Learning the Geodesic Path for Incremental Learning (2021, background): “The gradual changes between two different tasks can be modeled with the geodesic flow using projection to intermediate subspaces [9].”
An introduction to domain adaptation and transfer learning (2018, methodology): “Computing the direction of the geodesic is performed using matrix exponentials or something called spline flow [67,36].”
Riemannian Optimization on Tensor Products of Grassmann Manifolds: Applications to Generalized Rayleigh-Quotients (2010, methodology): “[10] have developed an efficient method to compute the matrix exponential, reducing the complexity order to O(nm(2)) (m < n).”
A Blur-Robust Descriptor with Applications to Face Recognition (2012, methodology): “However, since the expression for the inverse exponential map is not available analytically for the Grassmann manifold, we use a numerical method [14] as given in Algorithm 1.”
Statistical Computations on Grassmann and Stiefel Manifolds for Image and Video-Based Recognition (2011, unknown): “[41].”