Traditional numerical methods for calculating matrix eigenvalues are prohibitively expensive for high-dimensional problems. Iterative random sparsification 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 several benchmark problems in quantum chemistry.

翻译：对于高维问题,传统的计算电子元值矩阵的数值方法过于昂贵,高维问题过于昂贵,循环性随机喷雾方法通过利用反复随机抽样和平均法,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,并展示其在量子化学若干基准问题方面的性能。