Traditional numerical methods for calculating matrix eigenvalues are prohibitively expensive for high-dimensional problems. Randomized iterative methods allow for the estimation of a single dominant eigenvalue at reduced cost by leveraging repeated random sampling and averaging. We present a general approach to extending such methods for the estimation of multiple eigenvalues and demonstrate its performance for problems in quantum chemistry with matrices as large as 28 million by 28 million.

翻译：对于高维问题,传统的计算电子元值矩阵的数字方法过于昂贵,难以承受。随机迭代方法通过利用反复随机采样和平均法,可以以较低的成本估算单一主要电子元值。我们提出了一个总体方法,以扩大这种估算多种电子元值的方法,并用高达2 800万到2 800万的基数来显示其在量子化学问题方面的性能。