For Hermitian matrices, the optimal block subspace expansion that minimizes all principal angles to a target invariant subspace is explicitly characterized, with convergence bounds and computable Rayleigh-Ritz versions.
Jia, The convergence of generalized Lanczos methods for large unsymmetric eigenproblems, SIAM Journal on Matrix Analysis and Applications 16 (1995), 843–862
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Block subspace expansions for eigenvalues and eigenvectors approximation
For Hermitian matrices, the optimal block subspace expansion that minimizes all principal angles to a target invariant subspace is explicitly characterized, with convergence bounds and computable Rayleigh-Ritz versions.