Bootstrapped Block Lanczos for large-dimension eigenvalue problems

The Lanczos algorithm has proven itself to be a valuable matrix eigensolver for problems with large dimensions, up hundreds of millions or even tens billions. computational cost using any is dominated by the number sparse matrix-vector multiplications required reach suitable convergence. Block replaces multiplication matrix-matrix multiplication; multplication more efficient, due improved data locality and amortizing fetching constructing element, but randomly chosen starting block (or pivot), requires We find that bootstrapped pivot block, is, an initial constructed from approximate eigenvectors computed in truncated space, leads dramatically reduced multiplications, significantly outperforming both standard vector random pivot. A key condition speed-up have non-trivial overlap final converged vector. implement this approach configuration-interaction code nuclear structure, reduction time-to-solution factor two more, ten.