Shift-Invert Arnoldi Approximation to the Toeplitz Matrix Exponential
SIAM Journal on Scientific Computing
On the Convergence of Krylov Subspace Methods for Matrix Mittag-Leffler Functions
SIAM Journal on Numerical Analysis
Using the Restricted-denominator Rational Arnoldi Method for Exponential Integrators
SIAM Journal on Matrix Analysis and Applications
Computation of matrix functions with deflated restarting
Journal of Computational and Applied Mathematics
Preconditioning linear systems via matrix function evaluation
Applied Numerical Mathematics
A family of Adams exponential integrators for fractional linear systems
Computers & Mathematics with Applications
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In this paper we are interested in the polynomial Krylov approximations for the computation of $\varphi(A)v$, where $A$ is a square matrix, $v$ represents a given vector, and $\varphi$ 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.