Before revision:  The complex-step approximation of the Jacobian is applied to the Krylov-based KIOPS (Krylov with incomplete orthogonalization procedure solver) algorithm for computing matrix-vector products with \varphi -functions. Results are evaluated using standard benchmarks .
After revision:  The complex-step approximation of the Jacobian is applied to the Krylov-based KIOPS (Krylov with incomplete orthogonalization procedure solver) algorithm for computing matrix-vector products with \varphi . Performance of the new numerical methods is evaluated using a set of standard benchmark tests .