Nyström's method always yields higher-accuracy leading eigenvalues than Rayleigh-Ritz for positive semi-definite matrices given a subspace approximation, with improvements that can be arbitrarily large.
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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.
CUTS-GPR performs numerically exact Gaussian process regression with near-linear scaling in training points N and low-order polynomial scaling in dimensions D by exploiting additive kernels on incomplete grids.
citing papers explorer
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Finding accurate eigenvalues and eigenvectors of positive semi-definite matrices given a subspace
Nyström's method always yields higher-accuracy leading eigenvalues than Rayleigh-Ritz for positive semi-definite matrices given a subspace approximation, with improvements that can be arbitrarily large.
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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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Don't Get Your Kroneckers in a Twist: Gaussian Processes on High-Dimensional Incomplete Grids
CUTS-GPR performs numerically exact Gaussian process regression with near-linear scaling in training points N and low-order polynomial scaling in dimensions D by exploiting additive kernels on incomplete grids.