  The stochastic Lanczos quadrature method has garnered significant attention
recently. Upon examination of the error analyses given by Ubaru, Chen and Saad
and Cortinovis and Kressner, certain notable inconsistencies arise. It turns
out that the former's results are valid for cases with symmetric quadrature
nodes and may not be adequate for many practical cases such as estimating log
determinant of matrices. This paper analyzes probabilistic error bound of the
stochastic Lanczos quadrature method for cases with asymmetric quadrature
nodes. Besides, an optimized error allocation technique is employed to minimize
the overall number of matrix vector multiplications required by the stochastic
Lanczos quadrature method.
