Convergence of Eigenvector Continuation

Eigenvector continuation is a computational method that finds the extremal eigenvalues and eigenvectors of Hamiltonian matrix with one or more control parameters. It does this by projection onto subspace corresponding to selected training values The has proven be very efficient accurate for interpolating extrapolating eigenvectors. However, almost nothing known about how converges, its rapid convergence properties have remained mysterious. In letter we present first study eigenvector continuation. order perform mathematical analysis, introduce new variant call vector We prove identical then analyze Our analysis shows that, in general, converges rapidly than perturbation theory. faster achieved eliminating phenomenon differential folding, interference between non-orthogonal vectors appearing at different orders From our can predict both inside outside radius While non-perturbative method, show rate deduced from power series expansions results also yield insights into nature divergences