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.

翻译：随机Lanczos求积法近年来引起了广泛关注。通过审视Ubaru、Chen与Saad以及Cortinovis与Kressner给出的误差分析，发现其中存在显著的不一致性。前者结果的适用条件限定于对称求积节点情形，可能难以满足诸如矩阵对数行列式估计等实际应用需求。本文针对非对称求积节点情形，分析了随机Lanczos求积法的概率误差界。此外，采用优化误差分配技术，以最小化随机Lanczos求积法所需的矩阵向量乘法总次数。