论文标题
一种快速迭代算法，用于近乎基因的特征值问题
A fast iterative algorithm for near-diagonal eigenvalue problems
论文作者
论文摘要
我们引入了一种新型的特征值算法，该算法是受瑞利 - schrödinger扰动理论启发的近乎基因矩阵的，并称为迭代扰动理论（IPT）。与标准的特征值算法相反，这些算法要么是“直接”（计算所有特征台）或“迭代”（仅计算几个），IPT计算了具有相同基本迭代过程的任何数量的特征。由于这种完美的并行性，IPT比经典方法（用于全光谱问题的Lapack或Cusolver，对极端特征值的戴维森求解器）更有效。我们提供了足够的线性收敛条件，并在致密和稀疏的测试矩阵上（包括量子化学的一个）表现出表现。
We introduce a novel eigenvalue algorithm for near-diagonal matrices inspired by Rayleigh-Schrödinger 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.
