The computation of approximating e^tA B, where A is a large sparse matrix and B is a rectangular matrix, serves as a crucial element in numerous scientific and engineering calculations. A powerful way to consider this problem is to use Krylov subspace methods. The purpose of this work is to approximate the matrix exponential and some Cauchy-Stieltjes functions on a block vectors B of R^n*p using a rational block Lanczos algorithm. We also derive some error estimates and error bound for the convergence of the rational approximation and finally numerical results attest to the computational efficiency of the proposed method.

翻译：计算近似e^tA B（其中A为大型稀疏矩阵，B为矩形矩阵）是众多科学与工程计算中的关键环节。处理该问题的一种有效途径是采用Krylov子空间方法。本文旨在利用有理块Lanczos算法，对R^n×p空间中的块向量B近似计算矩阵指数及若干Cauchy-Stieltjes函数。我们进一步推导了有理近似收敛性的误差估计与误差界，最终数值实验结果验证了所提方法的计算效率。