Eigenvector Continuation
Eigenvector continuation, recently introduced into physics by Frame et al. is a powerful (yet strikingly simple in practice) method to address physics problems which are otherwise not feasible. Based on analytic function theory, it exploits small amounts of information contained in eigenvectors far away (in some parameter space controlling the difficulty of the calculation) from the physical point of interest, enabling a robust extrapolation to this point. In an actual implementation, the essence of the system is “learned” through the construction of a highly effective (non-orthogonal) basis, enabling a variational calculation of the states of interest.
As a novel techniques, eigenvector continuation provides ample opportunity for applications which have so far not been considered. Exploring such applications and understanding better the systematics that make eigenvector continuation so powerful is a current focus point of my research.