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arXiv · 2012.14702

A fast iterative algorithm for near-diagonal eigenvalue problems

Maseim Kenmoe·Ronald Kriemann·Matteo Smerlak·Anton S. Zadorin
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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.

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Maseim Kenmoe, Ronald Kriemann, Matteo Smerlak, Anton S. Zadorin. 2020-12-29. A fast iterative algorithm for near-diagonal eigenvalue problems. https://doi.org/10.1137/21m1401474

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