论文标题
随机块Krylov空间方法用于跟踪和日志测定估计器
Randomized block Krylov space methods for trace and log-determinant estimators
论文作者
论文摘要
我们提出基于块Krylov空间方法的随机算法，用于估计遗传学阳性半明确矩阵的痕量和对数确定因子。使用Chebyshev多项式和高斯随机矩阵的性质，我们提供了提出的估计器的误差分析，并获得了期望和浓度误差界限。这些界限改善了文献中给出的相应界限。提出了数值实验，以说明算法的性能并测试误差界限。
We present randomized algorithms based on block Krylov space method for estimating the trace and log-determinant of Hermitian positive semi-definite matrices. Using the properties of Chebyshev polynomial and Gaussian random matrix, we provide the error analysis of the proposed estimators and obtain the expectation and concentration error bounds. These bounds improve the corresponding ones given in the literature. Numerical experiments are presented to illustrate the performance of the algorithms and to test the error bounds.
