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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OSI alone does not yield relative-error guarantees for sketching; counterexamples for least-squares and randomized SVD show that upper control on the optimal residual is required to recover near-relative error.
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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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Oblivious Subspace Injection Is Not Enough for Relative Error
OSI alone does not yield relative-error guarantees for sketching; counterexamples for least-squares and randomized SVD show that upper control on the optimal residual is required to recover near-relative error.