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

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.