  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.
