Randomized block Krylov subspace methods for trace and log-determinant estimators

We present randomized algorithms based on block Krylov subspace methods for estimating the trace and log-determinant of Hermitian positive semi-definite matrices. Using the properties of Chebyshev polynomials 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.

Automated summary

This paper presents randomized algorithms based on block Krylov subspace methods for estimating the trace and log-determinant of Hermitian positive semi-definite matrices. The error analysis of the proposed estimators, utilizing Chebyshev polynomials and Gaussian random matrices, provides improved expectation and concentration error bounds compared to existing literature. Numerical experiments confirm the performance of the algorithms and validate the error bounds.