Error estimates for polynomial Krylov approximations to matrix functions

In this paper we are interested in the polynomial Krylov approximations for the computation of φ(A)v, where A is a square matrix, v represents a given vector, and φ is a suitable function which can be employed in modern integrators for differential problems. Our aim consists of proposing and analyzing innovative a posteriori error estimates which allow a good control of the approximation procedure. The effectiveness of the results we provide is tested on some numerical examples of interest.