A fast iterative algorithm for near-diagonal eigenvalue problems
Numerical Analysis
2022-11-18 v4 Numerical Analysis
Abstract
We introduce a novel eigenvalue algorithm for near-diagonal matrices inspired by Rayleigh-Schr\"odinger perturbation theory and termed Iterative Perturbative Theory (IPT). Contrary to standard eigenvalue algorithms, which are either 'direct' (to compute all eigenpairs) or 'iterative' (to compute just a few), IPT computes any number of eigenpairs with the same basic iterative procedure. Thanks to this perfect parallelism, IPT proves more efficient than classical methods (LAPACK or CUSOLVER for the full-spectrum problem, preconditioned Davidson solvers for extremal eigenvalues). We give sufficient conditions for linear convergence and demonstrate performance on dense and sparse test matrices, including one from quantum chemistry.
Cite
@article{arxiv.2012.14702,
title = {A fast iterative algorithm for near-diagonal eigenvalue problems},
author = {Maseim Kenmoe and Ronald Kriemann and Matteo Smerlak and Anton S. Zadorin},
journal= {arXiv preprint arXiv:2012.14702},
year = {2022}
}