A Fast Iterative Algorithm for Near-Diagonal Eigenvalue Problems

We introduce a novel eigenvalue algorithm for near-diagonal matrices inspired by Rayleigh–Schrödinger perturbation theory and termed iterative perturbative (IPT). Contrary to standard algorithms, which are either “direct” (to compute all eigenpairs) or “iterative” just few), IPT computes any number of eigenpairs with the same basic procedure. Thanks this perfect parallelism, proves more efficient than classical methods (LAPACK CUSOLVER full-spectrum problem, preconditioned Davidson solvers extremal eigenvalues). give sufficient conditions linear convergence demonstrate performance on dense sparse test matrices, including one from quantum chemistry. The code is available at http://github.com/msmerlak/IterativePerturbationTheory.jl.