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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Three new refined and refined-harmonic JDGSVD algorithms (RCPF-JDGSVD, RCPF-HJDGSVD, RIF-HJDGSVD) are introduced for several GSVD components of large regular matrix pairs, with thick-restart implementations.
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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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Refined and refined harmonic Jacobi--Davidson methods for computing several GSVD components of a large regular matrix pair
Three new refined and refined-harmonic JDGSVD algorithms (RCPF-JDGSVD, RCPF-HJDGSVD, RIF-HJDGSVD) are introduced for several GSVD components of large regular matrix pairs, with thick-restart implementations.