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The Jacobi-Davidson method is a widely used subspace method for computing a few eigenpairs of a large, sparse, non-Hermitian matrix closest to a target. Like other subspace methods, it orthogonalizes each new expansion vector against the whole search basis, at a cost that grows quadratically with the subspace dimension...
This QR-based leverage score sampling method outperforms previously published schemes as it does not, in principle, require the resampling of the target tensor or recomputing the leverage scores of the KRP, minimizing the computational and storage overhead of the CPD-ALS procedure.
Iterative diagonalization is the dominant cost of plane-wave density-functional theory (DFT), with search-space orthogonalization scaling particularly quickly with problem size and the number of target states. We present a randomized block Davidson-type eigensolver that replaces Euclidean orthogonalization with randomi...
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