The Alpha-Procrustes geometry at alpha=1 produces Riemannian Hessians whose eigenvalues are uniformly bounded independent of the SPD matrix condition number, provided the Euclidean Hessian satisfies uniform spectral bounds.
SIAM Journal on Matrix Analysis and Applications 40(4), 1353–1370 (2019)
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Riemannian Optimization over Symmetric Positive Definite Matrices with the Alpha-Procrustes Geometry
The Alpha-Procrustes geometry at alpha=1 produces Riemannian Hessians whose eigenvalues are uniformly bounded independent of the SPD matrix condition number, provided the Euclidean Hessian satisfies uniform spectral bounds.