Talks and Poster Presentations (without Proceedings-Entry):
W. Auzinger, T. Jawecki, O. Koch:
"Computable upper error bounds for Krylov subspace approximations to matrix exponentials";
Talk: SciCADE 2019, International Conference on Scientific Computation and Differential Equations,
The reliability of well-known a posteriori error estimates for Krylov approximations to the matrix
exponential is discussed. In many cases error estimates constitute upper error bounds and even can
be tightened. Additionally, a new defect-based a posteriori error estimate is introduced. This error
estimate constitutes an upper norm bound on the error without further assumptions and can be
computed during the construction of the Krylov subspace with nearly no computational effort.
The matrix exponential function itself can be understood as a time propagation with restarts. In practice, we are interested in finding time steps for which the error of the Krylov subspace approximation
is smaller than a given tolerance. Apart from step size control, the new upper error bound can be
used on the fly to test if the dimension of the Krylov subspace is already sufficiently large to solve the
problem in a single time step with the required accuracy.
Created from the Publication Database of the Vienna University of Technology.