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The computation of approximating e^tA B, where A is a large sparse matrix andB is a rectangular matrix, serves as a crucial element in numerous scientificand engineering calculations. A powerful way to consider this problem is to useKrylov subspace methods. The purpose of this work is to approximate the matrixexponential and some Cauchy-Stieltjes functions on a block vectors B of R^n*pusing a rational block Lanczos algorithm. We also derive some error estimatesand error bound for the convergence of the rational approximation and finallynumerical results attest to the computational efficiency of the proposedmethod.

A Rational Krylov Subspace Method for the Computation of the Matrix Exponential Operator