Introduces Riemannian Nyström approximation via subspace projections and Haar-Grassmann sketching for tangent operators, plus a randomized Newton method, tested on SPD and Grassmann manifolds.
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This paper isolates admissibility conditions for trust-region radius updates that guarantee first-order stationarity and O(ε^{-2}) complexity, verifies them across five mechanism classes, and extends prior frameworks with new convergence results under linear Hessian growth.
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Nystr\"om Approximation on Manifolds
Introduces Riemannian Nyström approximation via subspace projections and Haar-Grassmann sketching for tangent operators, plus a randomized Newton method, tested on SPD and Grassmann manifolds.
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A survey of trust-region radius update mechanisms. Part I: First-order analysis
This paper isolates admissibility conditions for trust-region radius updates that guarantee first-order stationarity and O(ε^{-2}) complexity, verifies them across five mechanism classes, and extends prior frameworks with new convergence results under linear Hessian growth.