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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APLICUR uses one modest sketch to adaptively update a CUR preconditioner interleaved with LSQR iterations, delivering convergence guarantees independent of sketch size for general large-scale least-squares problems.
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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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Adaptive LSQR Preconditioning from One Small Sketch
APLICUR uses one modest sketch to adaptively update a CUR preconditioner interleaved with LSQR iterations, delivering convergence guarantees independent of sketch size for general large-scale least-squares problems.