We examine and compare several iterative methods for solving large-scale eigenvalue problems arising from nuclear structure calculations. In particular, we discuss the possibility of using block Lanczos method, a Chebyshev filtering based subspace iterations and the residual minimization method accelerated by direct inversion of iterative subspace (RMM-DIIS) and describe how these algorithms compare with the standard Lanczos algorithm and the locally optimal block preconditioned conjugate gradient (LOBPCG) algorithm. Although the RMM-DIIS method does not exhibit rapid convergence when the initial approximations to the desired eigenvectors are not sufficiently accurate, it can be effectively combined with either the block Lanczos or the LOBPCG method to yield a hybrid eigensolver that has several desirable properties. We will describe a few practical issues that need to be addressed to make the hybrid solver efficient and robust.

翻译：我们研究并比较了几种用于求解核结构计算中大规模特征值问题的迭代方法。具体而言，我们探讨了使用分块Lanczos法、基于切比雪夫滤波的子空间迭代法以及通过迭代子空间直接求逆加速的残差最小化方法（RMM-DIIS）的可能性，并描述了这些算法与标准Lanczos算法和局部最优分块预处理共轭梯度（LOBPCG）算法的对比情况。尽管当所需特征向量的初始近似不够精确时，RMM-DIIS方法收敛速度较慢，但它可以与分块Lanczos法或LOBPCG方法有效结合，形成一种具有多种理想特性的混合特征求解器。我们将介绍一些实际应用中的关键问题，以确保该混合求解器高效且稳健。