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.

翻译：我们引入了一种由雷利-施特尔“扰动理论”和称为“迭代干涉理论(IPT)”所启发的近二角基体的新型电子价值算法。 与标准的电子价值算法相反,这种算法要么是“直接”(计算所有电子元),要么是“线性”(计算少数),它计算出具有相同基本迭接程序的任何数量。 由于这种完美的平行主义,IPT证明比古典方法(用于全谱问题的LAPACK或CUSOLVER,为极端电子元值设定的Davidson解算器)更有效。 我们为线性趋同提供了充分的条件,并展示了密度和稀薄测试基体的性能,包括量化学的性能。